The square root of 800 can be determined by the long division method, as 800 is not a perfect square number. A perfect square number is a number which can be written as a square of a particular number. The square root of a number is just the opposite of squaring. If a² = b, then b^1/2 = a. In radical form, the square root of 800 is denoted as √800, and in the exponential form, it is written as (800)^½. In this article, we shall learn how to find the square root of 800.

Learn more about square and square roots.

What is Square Root of 800?

The square root of 800 is a number whose square gives the result 800. Now, 800 is not a perfect square number because we cannot find any whole number which could be multiplied twice to get 800. Thus, we find an approximate value of the square root of 800 as it is an irrational number.

The square root of 800 can also be expressed as the roots of the quadratic equation

x² – 800 = 0

⇒ x² = 800

Taking the square root on both sides, we get

⇒ x = √800

⇒ x = ±20√2.

How to Find the Square Root of 800?

Let us find the square root of 800 using the prime factorisation and long division method. The repeated subtraction method will not work as 800 is not a perfect square, and its square root is an irrational number.

Prime Factorisation Method

To find the square root of 800 by the prime factorisation method, we first prime factorise 800 and then make pairs of two to get the square root.

Prime factorisation of 800 = 2 × 2 × 2 × 2 × 2 × 5 × 5

Square root of 800 = √[2 × 2 × 2 × 2 × 2 × 5 × 5] = 2 × 2 × 5 × √2 = 20√2.

Long Division Method

To find the square root of 800 by the long division method, we shall write 800 as a dividend and pair its digits from right to left. Now, we have to calculate the square root of 800:

To learn how to find the square root of any number long division method, click here.

Video Lessons on Square Root

Visualising square roots

10,049

Finding Square roots

67,622

Related Articles

• Square Root 1 to 100
• Trick to Find Square Root
• Square Root Table
• Square Root Calculator

Solved Examples on Square Root of 800

Example 1:

Find the perimeter of the circle whose area is 800𝜋 m².

Solution:

Let r be the radius of the circle.

The area of the circle = 𝜋r² = 800𝜋 m²

⇒ r² = 800 (taking square root on both the sides)

⇒ r = √800

⇒ r = 20√2 m (taking the positive root as length cannot be negative)

∴ the perimeter of the circle = 2𝜋r = 2 × 𝜋 × 20√2 = 40𝜋√2 m

Example 2:

Find the roots of the equation (x² – 2x)/4 = (400 – x)/2.

Solution:

We have (x² – 2x)/4 = (400 – x)/2

⇒ 2x² – 4x = 1600 – 4x

⇒ 2x² – 1600 = 0

⇒ x² – 800 = 0

⇒ x = √800 = ±20√2

∴ x = 20√2 and –20√2.

Example 3:

What is the smallest number that should be multiplied with 800 to make it a perfect square number? Also, find the square root of that number obtained.

Solution:

Now, the square root of 800 = 20√2.

Then 800 × 2 = 1600 will be the perfect square number. Thus, 2 is the smallest number that should be multiplied.

√1600 = 40.