Square Root of 160

There are many ways to calculate the square root of 160. Here, we will explore three approaches that provide a good approximation. Any number that can be expressed as the square of another integer is said to be a perfect square number. The square root of 160 is irrational since it is not a square number. The opposite of squaring is what is known as a number’s square root. The square root of 160 is expressed as √160 in radical form and as (160)^½ in exponential form. We will explore how to calculate the square root of 160 in this article.

What is the Square Root of 160?

The number whose square produces the value 160 is called the square root of 160. The number 160 is not a perfect square. As 160 is an irrational number, we calculate a rough approximation for its square root.

The quadratic equation x² – 160 = 0 may also be used to represent the square root of 160.

⇒ x² = 160

Now, take the square root on both sides, we get

⇒ x = √160

⇒ x = ± 12.649.

Also, try out: Square Root Calculator.

How to Calculate the Square Root of 160?

Let’s use the Newton formula, long division and prime factorization method to get the square root of 160. Since 160 is not a perfect square and its square root is an irrational number, the repeated subtraction approach will not work.

Finding Square Root of 160 Using Newton’s Equation

We employ Newton’s equation to get a number’s estimated square root for values that are not perfect squares. The Newton’s equation is written as,

√N ≈ ½ (N/A + A),

where

N is the integer whose square root we need to calculate.

A is the approximate square root estimate.

Here, N = 160 and A = 12, since 12² = 144 < 160. Let’s substitute these numbers in the formula to get a close approximation to find the square root of 160.

√160 ≈ ½ (160/12 + 12)

√160 ≈ ½ (13.33 + 12)

√160 ≈ 25.33/2

√160 ≈ 12.66.

This approach of calculating square roots is sometimes referred to as the approximation approach.

Finding Square Root of 160 by Prime Factorisation Method

By using the prime factorization technique, we can calculate the square root of 160 by first prime factorising the number. As 160 is a composite number, its prime factors are as follows:

The prime factorisation of 160 = 2 × 2 × 2 × 2 × 2 × 5 or 2⁵ × 5

Square root of 160 = √[2 × 2 × 2 × 2 × 2 × 5] = 2 × 2 × √10

Square root of 160 = 4√10.

Finding Square Root of 160 by Long Division Method

By using the long division approach, we may get the square root of 160 by writing 160 as a dividend and pairing its digits from right to left. We must now determine the square root of 160:

Thus, √160 = 12.64 (approximately).

To determine the square root of any number using the long division technique, check out the following link:

• Long Division Method to Find the Square Root of a Number.

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Solved Examples on Square Root of 160

Example 1:

What is the perimeter of a circle whose area is 160𝜋 m².

Solution:

Assume that “r” be the radius of the circle.

We know that the area of the circle is 𝜋r²

I.e., 𝜋r² = 160𝜋 m²

Now, cancel out 𝜋 on both sides of the equation, we get,

⇒ r² = 160

Now, take the square root on both sides.

⇒ r = √160

⇒ r = + 12.64 m or – 12.64

Since, the length cannot be in negative value, we take r = 12.64.

Now, substitute r = 12.64 m in the perimeter of a circle formula,

The perimeter of the circle = 2𝜋r

P = 2 × 3.14 × 12.64

P = 79.38 m (approx.).

Thus, the perimeter of a circle is approximately equal to 79.38 m.

Example 2:

Determine the roots of the equation (a² – 10a)/10 = (16.0 – a).

Solution:

Given equation: (a² – 10a)/10 = (16.0 – a)

On simplifying the given equation, we get,

⇒ a² – 10a = 160 – 10a

⇒ a² – 160 = 0

⇒ a² = 160

Taking square root on both sides, we get

⇒ a = √160 = ±12.64

Therefore, the roots of the given equation is:

a = 12.64 and a = -12.64.

Example 3:

What is the least number that has to be subtracted from 160 to make it a perfect square number? Furthermore, calculate the square root of the result.

Solution:

As we know, 12² = 144 < 160.

Hence, we should subtract 16 from 160.

Therefore, 160 – 16 = 144, which is a perfect square number.

Thus, the square root of 144, √144 is 12.