Square Root of 7
In Mathematics, the square root of 7 is a number, which is multiplied by itself for two times results in the original number 7. To find the square root of the given number, we need to know if it is a perfect square or not. Number 7 is not a perfect square. Therefore, we have to find the square root of 7 using the long division method. In this article, we are going to learn how to find the value of square root 7 using the long division method with complete explanation.
What is the Value of Square Root of 7?
The value of square root of 7 is a number which when multiplied by itself two times results in the original number. Symbolically, the square root of 7 is expressed as √7. In other words, the radical form of square root of 7 is √7.
√7 = √(Number × Number)
Thus, if we multiply 2.645 two times, we obtain the number 7.
(i.e) √7 = √(2.645×2.645)
√7 = √(2.645)2
Now, cancel out square and square root, we get
√7 = 2.645.
Thus, the square root of 7, √7 is approximately equal to 2.645.
Square Root of 7 in Decimal Form: 2. 645 |
Square Root of 7 by Long Division Method
Since the number 7 is not a perfect square number, the square root of 7 is found using the long division method. Now, follow the below steps to find the value of √7.
- First, write the number 7 in decimal form. (i.e) 7. 0000
- Now, divide the number 7 by a number such the product of same number should be smaller than or equal to 7. Thus, 2×2 = 4, which is smaller than 7.
- Now, subtract 4 from 7, we will get the remainder 3 and quotient 2.
- Now, double the quotient and we get 4 and assume that 40 is the new divisor.
- Bring down two zeros and we get 300 is our new dividend.
- Now, find the number, such that (40+ new number)×new number should be less than or equal to 300. Hence, (40+6)×6 = 276. Hence, 276 < 300.
- Again, subtract 276 from 300. Hence, we get a remainder of 24 and the quotient is 26.
- Repeat this same process until we get the value of square root of 7 up to 3 decimal places. (Put the decimal point in the quotient once the division process is completed).
- Thus, the value of square root of 7 is approximately equal to 2.645.
Examples
Example 1:
Simplify the expression: 2√7 + 5√7.
Solution:
Given: 2√7 + 5√7.
2√7+5√7 = 7√7.
We know that √7 is approximately equal to 2.645.
Now, substitute the value, we 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 [Since, √7 = 2.645]
a = 3
Hence, the value of a is 3.
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Frequently Asked Questions on Square Root of 7
What is the approximate value of square root of 7?
The value of square root of 7 is approximately equal to 2.645 (Rounded to 3 decimal places).
Is √7 a rational or irrational number?
√7 is an irrational number, as the value of √7 cannot be expressed in the form of p/q.
What is the value of square of square root of 7?
The square of square root of 7 is 7.
(i.e) (√7)^{2} = 7.
Is 7 a perfect square number?
No, 7 is not a perfect square number.
What is the value of 7 plus square root of 7?
We know that √7 = 2.645
Thus, 7+√7 = 7+2.645 = 9.645.