Square Root of 6400

The square root of 6400 is a number, which when multiplied by itself results in the number 6400. The square root of 6400 is a rational number as it can be expressed in the form of p/q. Here, we are going to discuss the value of the square root of 6400 and the methods such as prime factorization and the long division method to find the square root of 6400 are explained here in detail.

Table of Contents:

• What Is The Square Root Of 6400?
• Square Root Of 6400 In Radical Form
• Square Root Of 6400 By Prime Factorization Method
• Square Root Of 6400 By Long Division Method
• Solved Examples
• Practice Questions
• FAQs

What is the Square Root of 6400?

The square root of 6400 is a number, which when multiplied by itself and results in the number 6400. The square root of 6400 is symbolically expressed as √6400.

Hence, √6400 = √(Number × Number)

Thus, if we multiply the number 80 two times, we get the original value 6400.

(i.e) √6400 = √(80 × 80)

√6400 = √(80)²

Now, remove square and square root, we get

√6400 = ± 80

Square Root of 6400 in Radical Form

The value of the square root of 6400 can also be expressed in radical form. The simplest radical form of the square root of 6400 is √6400. The radical form of the square root of 6400 can be written if we know the prime factorisation of 6400. Thus, the prime factorisation of 6400 is 2⁸×5². Hence, if we write the prime factorisation of 6400 in the radical form, it will not be in the simplest form.

Square Root of 6400 by Prime Factorization Method

To find the square root of 6400 using the prime factorization method, one must know the prime factorization of 6400. We know that the prime factorization of 6400 is 2⁸×5².

Thus, √6400 = √[2×2×2×2×2×2×2×2×5×5]

√6400 = √[(2×2)×(2×2)×(2×2)×(2×2)×(5×5)]

This can also be written as

√6400 = √(2)². √(2)². √(2)². √(2)². √(5)²

√6400 = 2×2×2×2×5 = 80.

Hence, the value of the square root of 6400 is 80.

Square Root of 6400 by Long Division Method

Follow the below steps to find the square root of 6400 using the long division method:

Step 1: Write the number 6400. Now, pair the number 6400 from right to left by putting the bar on the top of the number.

Step 2: Now, divide the number 64 by a number, such that the product of the same number should be less than or equal to 64. Thus, 8×8 =64, which is equal to 64. Thus, we obtained the quotient = 8 and remainder =0.

Step 3: Double the quotient value, so we get 16 and assume that 160 is the new divisor. Now, bring down the value 00 for division operation. So, the new dividend obtained is 00. Now, find the number, such that (160 + new number) × new number should give the product value, that should be less than or equal to 00. Hence, (160+0) × 0 = 0, which is equal to 00.

Step 4: Hence, the new quotient is 80 and the remainder is 0.

Step 5: Therefore, the value of the square root of 6400, √6400 is 80.

Video Lessons on Square Roots

Visualising square roots

Finding Square roots

Examples

Example 1:

Simplify √6400 – 50

Solution:

Given: √6400 – 50

We know that the value of the square root of 6400 is 80. Now, substitute the value in the above-given expression, we get

√6400 – 50 = 80 – 50

√6400 – 50 = 30.

Hence, the simplified form of √6400 – 50 is 30.

Example 2:

Find the value of a, if 20√6400 +a = 2000.

Solution:

Given: 20√6400 +a = 2000

We know that √6400 = 80.

Now, substitute the value in the above equation, we get

20(80) +a = 2000

1600 + a = 2000

a = 2000 – 1600

a = 400.

Hence, the value of a is 400.

Practice Questions

1. What is the value of 5 times square root of 6400?
2. Simplify: [5√6400]/80.
3. Find the value of a, if a√6400 +10 = 170.

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