## Radical equations

### Radical Equation entered :

√x+5+√20-x = 7

### Step by step solution :

### Step 1 :

#### Isolate a square root on the left hand side :

Original equation

√x+5+√20-x = 7

Isolate

√x+5 = -√20-x+7

### Step 2 :

#### Eliminate the radical on the left hand side :

Raise both sides to the second power

(√x+5)^{2} = (-√20-x+7)^{2}

After squaring

x+5 = 20-x+49-14√20-x

### Step 3 :

#### Get remaining radical by itself :

Current equation

x+5 = 20-x+49-14√20-x

Isolate radical on the left hand side

14√20-x = -x-5+20-x+49

Tidy up

14√20-x = -2x+64

### Step 4 :

#### Eliminate the radical on the left hand side :

Raise both sides to the second power

(14√20-x)^{2} = (-2x+64)^{2}

After squaring

3920-196x = 4x^{2}-256x+4096

### Step 5 :

#### Solve the quadratic equation :

Rearranged equation

4x^{2} - 60x + 176 = 0

This equation has two rational roots:

{x1, x2}={11, 4}

### Step 6 :

#### Check that the first solution is correct :

Original equation, root isolated, after tidy up

√x+5 = -√20-x+7

Plug in 11 for x

√(11)+5 = -√20-(11)+7

Simplify

√16 = 4

Solution checks !!

Solution is:

x = 11

### Step 7 :

#### Check that the second solution is correct :

Original equation, root isolated, after tidy up

√x+5 = -√20-x+7

Plug in 4 for x

√(4)+5 = -√20-(4)+7

Simplify

√9 = 3

Solution checks !!

Solution is:

x = 4

### Two solutions were found :

- x = 4
- x = 11

## Square Root of 20

The square root of 20 is expressed as √20 in the radical form and as (20)^{½} or (20)^{0.5} in the exponent form. The square root of 20 rounded up to 8 decimal places is 4.47213595. It is the positive solution of the equation x^{2} = 20. We can express the square root of 20 in its lowest radical form as 2 √5.

**Square Root of 20:**4.47213595499958**Square Root of 20 in exponential form:**(20)^{½}or (20)^{0.5}**Square Root of 20 in radical form:**√20 or 2 √5

### What Is the Square Root of 20?

The square root of 20 can be obtained by the number whose square gives the original number. What number that could be? It can be seen that, there are no integers whose square will give 20.

**√**20 = 4.472

To check this answer, we can find (4.472)^{2} and we can see that we get the number 19.998784 ... which is very close to 20 when it's rounded to its nearest value.

### Is the Square Root of 20 Rational or Irrational?

A rational number is either terminating or non-terminating and has a repeating pattern in its decimal part. We saw that **√**20 = 4.4721359549. This is non-terminating and the decimal part has no repeating pattern. So it is NOT a rational number. Hence, **√**20 is an irrational number.

### How to Find the Square Root of 20?

There are different methods to find the square root of any number. Click here to know more about it.

### Simplified Radical Form of Square Root of 20

20 is not a prime number. Thus it has more than two factors, 1, 2, 4, 5, 10 and 20. To find the square root of any number, we take one number from each pair of the same numbers from its prime factorization and we multiply them. The factorization of 20 is 2 × 2 × 5 which has 1 pair of the same number. Thus, the simplest radical form of **√**20 is 2**√**5 itself.

### Square Root of 20 by Long Division Method

The square root of 20 can be found using the long division as follows.

**Step 1**: Pair of digits of a given number starting with a digit at one's place. Put a horizontal bar to indicate pairing.**Step 2**:Now we need to find a number which on multiplication with itself gives a product of less than or equal to 20. As we know 4 × 4 = 16 < 20. Hence, the divisor is 4 and the quotient is 4.**Step 3**:Now, we have to bring down 00 and multiply the quotient by 2. This give us 8. Hence, 8 is the starting digit of the new divisor.**Step 4**: 4 is placed at one's place of new divisor because when 84 is multiplied by 4 we get 336. The obtained answer now is 64 and we bring down 00.**Step 5**: The quotient now becomes 44 and it is multiplied by 2. This gives 88, which then would become the starting digit of the new divisor.**Step 6**: 7 is placed at one's place of new divisor because on multiplying 887 by 7 we get 6209. This gives the answer 191 and we bring 00 down.**Step 7**: Now the quotient is 447 when multiplied by 2 gives 894, which will be the starting digit of the new divisor.**Step 8**: 2 is the new divisor because on multiplying 8942 by 2 we will get 17884. So, now the answer is 1216 and the next digit of the quotient is 2.

So far we have got **√**20 = 4.472. On repeating this process further, we get, **√**20 = 4.4721359549...

**Explore Square roots using illustrations and interactive examples**

**Important Notes:**

- 20 lies between 16 and 25. So
**√**20 lies between**√**16 and**√**25 i.e.,**√**20 lies between 16 and 25 - The prime factorization method is written as a square root of a non-perfect square number in the simplest radical form. For example: 20 = 2 × 2 × 5. So,
**√**20 =**√**2 × 2 × 5 = 2**√**5.

**Think Tank:**

- Is it possible the value of a square root can be negative as well?
- Is
**√**-20 a real number?

**Example 1**: Judy has a square-shaped room having an area of 20 square feet. What will be the length of the room's floor? Round your answer to the nearest tenth.**Solution**Let us assume that the length of the room is x feet. Then the area of the room's floor is x

^{2}square feet. By the given information:x

^{2 }= 20

x =**√**20 = 4.5 feetThe final answer is rounded to the nearest tenth. Hence, the length of the room is 4.5 feet.

**Example 2**: If the area of a circle is 20π square inches. What is its radius?**Solution**Then area is found using the formula of area of a circle is πr

^{2}square inches. By the given information,πr

^{2}= 20π

r^{2}= 20By taking the square root on both sides,

**√**r^{2}=**√**20. We know that the square root of r^{2}is r.

By calculating the square root of 20 is 4.47 inches.**Example:**If the area of a circle is 20π in^{2}. Find the radius of the circle.**Solution:**Let 'r' be the radius of the circle.

⇒ Area of the circle = πr^{2}= 20π in^{2}

⇒ r = ±√20 in

Since radius can't be negative,

⇒ r = √20

The square root of 20 is 4.472.

⇒ r = 4.472 in

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### FAQs on the Square Root of 20

### What is the Value of the Square Root of 20?

The square root of 20 is 4.47213.

### Why is the Square Root of 20 an Irrational Number?

Upon prime factorizing 20 i.e. 2^{2} × 5^{1}, 5 is in odd power. Therefore, the square root of 20 is irrational.

### What is the Square Root of 20 in Simplest Radical Form?

We need to express 20 as the product of its prime factors i.e. 20 = 2 × 2 × 5. Therefore, √20 = √2 × 2 × 5 = 2 √5. Thus, the square root of 20 in the lowest radical form is 2 √5.

### Is the number 20 a Perfect Square?

The prime factorization of 20 = 2^{2} × 5^{1}. Here, the prime factor 5 is not in the pair. Therefore, 20 is not a perfect square.

### Evaluate 4 plus 12 square root 20

The given expression is 4 + 12 √20. We know that the square root of 20 is 4.472. Therefore, 4 + 12 √20 = 4 + 12 × 4.472 = 4 + 53.666 = 57.666

### What is the Value of 2 square root 20?

The square root of 20 is 4.472. Therefore, 2 √20 = 2 × 4.472 = 8.944.

Here we will define, analyze, simplify, and calculate the square root of 20. We start off with the definition and then answer some common questions about the square root of 20. Then, we will show you different ways of calculating the square root of 20 with and without a computer or calculator. We have a lot of information to share, so let's get started!

**Square root of 20 definition**

The square root of 20 in mathematical form is written with the radical sign like this √20. We call this the square root of 20 in radical form. The square root of 20 is a quantity (q) that when multiplied by itself will equal 20.

√20= q × q = q

^{2}

**Is 20 a perfect square?**

20 is a perfect square if the square root of 20 equals a whole number. As we have calculated further down on this page, the square root of 20 is not a whole number.

20 is not a perfect square.

**Is the square root of 20 rational or irrational?**

The square root of 20 is a rational number if 20 is a perfect square. It is an irrational number if it is not a perfect square. Since 20 is not a perfect square, it is an irrational number. This means that the answer to "the square root of 20?" will have an infinite number of decimals. The decimals will not terminate and you cannot make it into an exact fraction.

√20is an irrational number

**Can the square root of 20 be simplified?**

You can simplify 20 if you can make 20 inside the radical smaller. We call this process "to simplify a surd". The square root of 20 can be simplified.

√20= 2√5

**How to calculate the square root of 20 with a calculator**

The easiest and most boring way to calculate the square root of 20 is to use your calculator! Simply type in 20 followed by √x to get the answer. We did that with our calculator and got the following answer with 9 decimal numbers:

√20 ≈ 4.472135955

**How to calculate the square root of 20 with a computer**

If you are using a computer that has Excel or Numbers, then you can enter SQRT(20) in a cell to get the square root of 20. Below is the result we got with 13 decimals. We call this the square root of 20 in decimal form.

SQRT(20) ≈ 4.4721359549996

**What is the square root of 20 rounded?**

The square root of 20 rounded to the nearest tenth, means that you want one digit after the decimal point. The square root of 20 rounded to the nearest hundredth, means that you want two digits after the decimal point. The square root of 20 rounded to the nearest thousandth, means that you want three digits after the decimal point.

10th: √20≈ 4.5

100th: √20≈ 4.47

1000th: √20≈ 4.472

**What is the square root of 20 as a fraction?**

Like we said above, since the square root of 20 is an irrational number, we cannot make it into an exact fraction. However, we can make it into an approximate fraction using the square root of 20 rounded to the nearest hundredth.

√20

≈ 4.47/1

≈ 447/100

**≈ 4 47/100**

**What is the square root of 20 written with an exponent?**

All square roots can be converted to a number (base) with a fractional exponent. The square root of 20 is no exception. Here is the rule and the answer to "the square root of 20 converted to a base with an exponent?":

√b= b

^{½}

√20= 20

^{½}

**How to find the square root of 20 by long division method**

Here we will show you how to calculate the square root of 20 using the long division method with one decimal place accuracy. This is the lost art of how they calculated the square root of 20 by hand before modern technology was invented.

**Step 1)**

Set up 20 in pairs of two digits from right to left and attach one set of 00 because we want one decimal:

**Step 2)**

Starting with the first set: the largest perfect square less than or equal to 20 is 16, and the square root of 16 is 4. Therefore, put 4 on top and 16 at the bottom like this:

**Step 3)**

Calculate 20 minus 16 and put the difference below. Then move down the next set of numbers.

**Step 4)**

Double the number in green on top: 4 × 2 = 8. Then, use 8 and the bottom number to make this problem:

8?× ?≤ 400

The question marks are "blank" and the same "blank". With trial and error, we found the largest number "blank" can be is 4. Now, enter 4 on top:

That's it! The answer is on top. The square root of 20 with one digit decimal accuracy is 4.4.

Square Root of a Number

Please enter another number in the box below to get the square root of the number and other detailed information like you got for 20 on this page.

**Notes**

Remember that negative times negative equals positive. Thus, the square root of 20 does not only have the positive answer that we have explained above, but also the negative counterpart.

We often refer to perfect square roots on this page. You may want to use the list of perfect squaresfor reference.

Square Root of 21

Here is the next number on our list that we have equally detailed square root information about.

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## 20 sqrt

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