In Mathematics, the square source of 7 is a number, which is multiply by chin for 2 times results in the original number 7. To discover the square root of the provided number, we require to know if that is a perfect square or not. Number 7 is no a perfect square. Therefore, we have to find the square root of 7 making use of the long department method. In this article, we are going to learn how to find the value of square source 7 using the long division method with complete explanation.

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What is the value of Square source of 7?

The value of square root of 7 is a number which as soon as multiplied through itself two times results in the original number. Symbolically, the square source of 7 is expressed together √7. In various other words, the radical type of square root of 7 is √7.

√7 = √(Number × Number)

Thus, if we multiply 2.645 two times, we achieve the number 7.

(i.e) √7 = √(2.645×2.645)

√7 = √(2.645)2

Now, cancel out square and square root, us get

√7 = 2.645.

Thus, the square source of 7, √7 is approximately equal to 2.645.

Square root of 7 in Decimal Form: 2. 645

Square source of 7 by Long department Method

Since the number 7 is no a perfect square number, the square root of 7 is discovered using the long division method. Now, follow the listed below steps to find the worth of √7.

First, write the number 7 in decimal form. (i.e) 7. 0000Now, divide the number 7 by a number together the product of very same number have to be smaller than or equal to 7. Thus, 2×2 = 4, i m sorry is smaller sized than 7.Now, subtract 4 native 7, us will get the remainder 3 and quotient 2.Now, twin the quotient and we gain 4 and also assume the 40 is the new divisor. Bring down 2 zeros and also we get 300 is our brand-new dividend.Now, find the number, such that (40+ new number)×new number must be less than or same to 300. Hence, (40+6)×6 = 276. Hence, 276 Again, subtract 276 from 300. Hence, we obtain a remainder that 24 and also the quotient is 26.Repeat this same procedure until we obtain the value of square source of 7 up to 3 decimal places. (Put the decimal point in the quotient as soon as the division process is completed).Thus, the value the square source of 7 is around equal to 2.645.

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Examples

Example 1: 

Simplify the expression: 2√7 + 5√7.

Solution:

Given: 2√7 + 5√7.

2√7+5√7 = 7√7.

We recognize that √7 is about equal come 2.645.

Now, substitute the value, us get

2√7+5√7 = 7(2.645) = 18.515.

Example 2: 

Find the value of a is a√7= 7.935.

Solution:

Given: a√7= 7.935

Thus, a = 7.935/√7

a = 7.935/2.645

a = 3

Hence, the value of a is 3.

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