# Square Root of 60: Simplified Radical Form

The number 60 is a composite even number. The value of square root 60 is 7.746. As the square root of a number x is denoted by √x, root 60 can be written as √60. In this section, we will learn how to calculate the square root of 60. Note that

• √60 = 7.746
• 601/2 is the exponential form of square root of 60.
• √60 is the radical form of square root of 60.
• The square root of 60 is 7.746 corrected up to 3 decimal places.
• 60 is not a perfect square.
• Square of 60: 60×60 = 3,600
• √60 is a quadratic surd.
• The simplified form of √60 is 2√15.

## Simplify square root of 60?

To find the square root of 60 in simplest radical form, we will express 60 as a product of perfect squares or as a product of a perfect square and  a non-perfect square.

Note that 60= 4×15 …(I)

Here 4 is a perfect square number as 4=22 and 15 is a non-perfect square.

Taking square root on both sides of (I), we get that

$\sqrt{60}=\sqrt{4 \times 15}$

$=\sqrt{4} \times \sqrt{15}$  $[\because \sqrt{a \times b}=\sqrt{a} \times \sqrt{b}]$

$=2 \times \sqrt{15}=2\sqrt{15}$

So the simplest radical form of the square root of 60 is 2√15.

## Is 60 a perfect square number?

We computed √60=2√15.

As √15 is not an integer, 60 is not a perfect square number.

Note that 60 is a non-perfect square number. This makes √60 is a quadratic surd.

## Is Square root of 60 Rational?

As √60=2√15 and √15 is not a rational number,  so the square root of 60 is not a rational number.

Actually, √60 is an irrational number.

## What is the value of root 60?

It is computed above that the simplest radical form of square root of 60 is 2√15.

We know √15=3.872

√60 = 2√15 = 2 × 3.872 = 7.746

So the value of the square root of 60 is equal to 7.746.

## Square root of 60 by Prime Factorization

To find the square root of 60 by the prime factorization method, we have to factorize the number 60. see that 60 is an even number, it will be divisible by 2.

So 60=2×30.

Now we will factorize 30 and similarly

30=2×15.

Finally, 15=3×5.

Combining all these we obtain that

60=2×2×3×5 …(II)

This is the prime factorization of 60.

Taking square root on both sides of (II), we get that

$\sqrt{60}=\sqrt{2 \times 2 \times 3 \times 5}$

$=\sqrt{2 \times 2} \times \sqrt{3 \times 5}$

$=2 \times \sqrt{15}$ $[\because \sqrt{a \times a}=a]$

$=2\sqrt{15}$

Therefore, the value of the square root of 60 is 2√15.

## FAQs on Square Root of 60

Q1: What is square root of 60 in radical form?

Answer: The square root of 60 in radical form is given by √60=2√15.

Q2: Is root 60 a quadratic surd?