The square root of 87 is expressed as √87 in the radical form and as (87)^{½} or (87)^{0.5} in the exponent form. The square root of 87 rounded up to 6 decimal places is 9.327379. It is the positive solution of the equation x^{2} = 87.

**Square Root of 87:**9.327379053088816**Square Root of 87 in exponential form:**(87)^{½}or (87)^{0.5}**Square Root of 87 in radical form:**√87

1. | What is the Square Root of 87? |

2. | How to find the Square Root of 87? |

3. | Is the Square Root of 87 Irrational? |

4. | FAQs |

## What is the Square Root of 87?

The square root of 87, (or root 87), is the number which when multiplied by itself gives the product as 87. Therefore, the square root of 87 = √87 = 9.327379053088816.

**☛ Check: Square Root Calculator**

## How to Find Square Root of 87?

### Value of √87 by Long Division Method

**Explanation:**

- Forming pair: 87
- Find a number Y (9) such that whose square is <= 87. Now divide 87 by 9 with quotient as 9.
- Now, let's find the decimal places after the quotient 9.
- Bring down the next pair 00, to the right of the remainder 6. The new dividend is now 600.
- Add the last digit of the quotient (9) to the divisor (9) i.e. 9 + 9 = 18. To the right of 18, find a digit Z (which is 3) such that 18Z × Z <= 600. After finding Z, together 18 and Z (3) form a new divisor 183 for the new dividend 600.
- Divide 600 by 183 with the quotient as 3, giving the remainder = 600 - 183 × 3 = 600 - 549 = 51.
- Bring down 00 again. Repeat above steps for finding more decimal places for the square root of 87.

Therefore, the square root of 87 by long division method is 9.3 approx.

## Is Square Root of 87 Irrational?

The actual value of √87 is undetermined. The value of √87 up to 25 decimal places is 9.327379053088815045554476. Hence, the square root of 87 is an irrational number.

**☛ Also Check:**

- Square Root of 784 - √784 = 28
- Square Root of 324 - √324 = 18
- Square Root of 361 - √361 = 19
- Square Root of 900 - √900 = 30
- Square Root of 65 - √65 = 8.06226
- Square Root of 225 - √225 = 15
- Square Root of 116 - √116 = 10.77033

## Square Root of 87 Solved Examples

**Example 1: Solve the equation x**^{2}− 87 = 0**Solution:**x

^{2}- 87 = 0 i.e. x^{2}= 87

x = ±√87

Since the value of the square root of 87 is 9.327,

⇒ x = +√87 or -√87 = 9.327 or -9.327.**Example 2: If the area of an equilateral triangle is 87√3 in**^{2}. Find the length of one of the sides of the triangle.**Solution:**Let 'a' be the length of one of the sides of the equilateral triangle.

⇒ Area of the equilateral triangle = (√3/4)a^{2}= 87√3 in^{2}

⇒ a = ±√348 in

Since length can't be negative,

⇒ a = √348 = 2 √87

We know that the square root of 87 is 9.327.

⇒ a = 18.655 in**Example 3: If the area of a square is 87 in**^{2}. Find the length of the side of the square.**Solution:**Let 'a' be the length of the side of the square.

⇒ Area of the square = a^{2}= 87 in^{2}

⇒ a = ±√87 in

Since length can't be negative,

⇒ a = √87 = 9.327 in

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## FAQs on the Square Root of 87

### What is the Value of the Square Root of 87?

The square root of 87 is 9.32737.

### Why is the Square Root of 87 an Irrational Number?

Upon prime factorizing 87 i.e. 3^{1} × 29^{1}, 3 is in odd power. Therefore, the square root of 87 is irrational.

### What is the Square of the Square Root of 87?

The square of the square root of 87 is the number 87 itself i.e. (√87)^{2} = (87)^{2/2} = 87.

### What is the Square Root of -87?

The square root of -87 is an imaginary number. It can be written as √-87 = √-1 × √87 = i √87 = 9.327i

where i = √-1 and it is called the imaginary unit.

### Evaluate 19 plus 6 square root 87

The given expression is 19 + 6 √87. We know that the square root of 87 is 9.327. Therefore, 19 + 6 √87 = 19 + 6 × 9.327 = 19 + 55.964 = 74.964

### What is the Square Root of 87 in Simplest Radical Form?

We need to express 87 as the product of its prime factors i.e. 87 = 3 × 29. Therefore, as visible, the radical form of the square root of 87 cannot be simplified further. Therefore, the simplest radical form of the square root of 87 can be written as √87