In Mathematics, the square root of 500, which is expressed as √500 in radical form, is defined as a number which, when multiplied by itself twice, results in the original number 500. The square root of 500 is an irrational number and it can also be represented as (500)½ or (500)0.5 in exponential form. Here, we are going to learn how to find the value of the square root of 500 using two methods, such as the prime factorisation method and long division method, in detail.
What is the Value of Square Root of 500?
The square root of 500 is approximately equal to 22.3606.
If we multiply the number 22.3606 twice, we get the original number 500.
(i.e) √500 = √(22.3606× 22.3606)
√500 = √(22.3606)2
Now, remove square and square root, we will get
√500 = ± 22.3606
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Square Root of 500 in Decimal Form: 22.3606. |
Radical Form of Square Root of 500
To write the √500 in radical form, first write the prime factorisation of 500. The prime factorisation of 500 is 22 × 53. On simplification, the square root of 500 in radical form is 10√5.
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Square Root of 500 in Radical Form: 10√5. |
Square Root of 500 by Prime Factorisation Method
To find the value of the square root of 500 using the prime factorization method, follow the below steps.
We know that the prime factorisation of 500 is 22 × 53, which is equal to 2×2×5×5×5.
Thus, √500 = √[(2 × 2)×(5)×(5×5)
√500 = √[(2)2×(5)2×5]
√500 = 2×5×√5.
√500 = 10√5.
Now, substitute the value of √5 in the above equation, we get
√500 = 10× 2.23606
√500 = 22.3606
Hence, the square root of 500 is approximately equal to 22.3606.
Square Root of 500 by Long Division Method
To find the square root of 500 using the long division method, follow the steps below:
Step 1: In decimal form, write the number 500. Pair the number 500.000000 by moving the bar from right to left across the top of the number.
Step 2: Next, divide 5 by a number such that the product of the two numbers must be less than or equal to 5. Hence, 2×2=4, which is less than 5. As a result, quotient = 2 and remainder = 1 are obtained.
Step 3: Doubling the quotient value gives us 4, therefore we will use 40 as the new divisor. Bring two zeros down for the division procedure now. As a result, the new dividend is 100. Determine the number that will result in a product that is less than or equal to 100. (i.e. (40 + new number)× new number).Hence, (40+2) × 2 = 84, which is less than 100 is used.
Step 4: Subtract 84 from 100. So we get a new remainder of 16 and a quotient of 22.
Step 5: Continue in this manner until the approximate value of the square root of 500 is obtained. (After bringing down all the values in the dividend, keep the decimal point in the quotient value.)
Step 6: As a result, the square root of 500 is approximately equal to 22.3606.
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Examples
Example 1:
Simplify the expression: 4√500.
Solution:
Given: (4√500).
As we know, √500 is 22.3606.
Substituting the value in the expression,
4√500 = 4(22.3606)
4√500 = 89.4424
Therefore, the simplification of 4√500 is 89.442.
Example 2:
Calculate the value of m, if m√500 – 5 = 210.
Solution:
Given: m√500 – 5 = 210…(1)
We know that √500 = 22.3606.
Now, substitute the value in equation (1), we get
m(22.3606) – 5 = 210
22.3606m = 215
m = 215/22.3606 = 9.6151
Therefore, the value of m is 9.6151.
Frequently Asked Questions on Square Root of 500
What is the value of the square root of 500?
The value of √500 is approximately equal to 22.3606.
How to express the square root of 500 in the simplest radical form?
The simplest radical form of √500 is 10√5.
Is 500 a perfect square?
No, 500 is a perfect square, since it cannot be expressed as the product of two equal integers.
Compute the value of 10 plus the square of square root of 500.
The value of the 10 plus square of square root of 500 is 510.
We know that (√500)2 = 500.
Hence, 10+500 = 510.
What is the value of square root of 500 minus 10?
We know that √500 is 22.3606.
Hence, 22.3606 – 10 = 12.3606.
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