Students can learn about Square roots and to work problems on the concept here.
The square root of a number results in a number which when multiplied with the same number gives the resultant number.
In math, If x2 = y ,We say that the square root of y is x and we write,$\sqrt{y}$ = x.
Thus,$\sqrt{4}$ = 2,$\sqrt{9}$ = 3.
Every non-negative real number x has a unique non-negative square root which is denoted with a radical sign as $\sqrt{x}$ .
In exponent form the square root is written as (x)1/2.Every positive number x has two square roots. One of them is +$\sqrt{x}$ , which is positive, and the other -$\sqrt{x}$ , which is negative. Together, these two roots are denoted $\pm$ $\sqrt{x}$ .
Square roots of integers that are not perfect squares are always irrational numbers, and have decimal values. Example $\sqrt{48}$ = 6.93
The term whose root is being considered is known as the radicand. In the expression $\sqrt{(xy-8)}$, (xy-8) is the radicand. The radicand is the number or expression under the radical sign.
Methods of Computing Square Roots
We can calculate square roots by using calculators, which have a square root key and Computer spreadsheets and other software. We can compute the square root of x using the identity
$\sqrt{(x)}$ = $e^{\frac{1}{2}lnx}$ or $\sqrt{(x)}$ = $10^{\frac{1}{2}logx}$
The most common iterative method of square root calculation by hand is known as the "Babylonian method" or "Heron's method" after the first century Greek philosopher Heron of Alexandria who first described it. It involves a simple algorithm, which results in a number closer to the actual square root each time it is repeated. To find r, the square root of a real number x:
Start with an arbitrary positive start value r (the closer to the square root of x, the better).
Replace r by the average between r and x/r, that is: $\frac{r+\frac{x}{r}}{2}$ (It is sufficient to take an approximate value of the average in order to ensure convergence.)
Repeat step 2 until r and x/r are as close as desired.
The time complexity for computing a square root with n digits of precision is equivalent to that of multiplying two n-digit numbers.
Algorithm to Find the Square Root
Consider $\sqrt17.64$
Step - 1 : To find the square root of a decimal number we put bars on the integral part (i.e., 17)of the number in the usual manner. And place bars on the decimal part (i.e., 64) on every pair of digits beginning with the first decimal place. Proceed as usual.We get 17.64.
Step - 2 : Now proceed in a similar manner. The left most bar is on 17 and 42 < 17 < 52.Take this number as the divisor and the number under the left-most bar as the dividend, i.e., 17. Divide and get the remainder.
Step - 3 : The remainder is 1. Write the number under the next bar (i.e., 64) to the right of this remainder, to get 164.
Step - 4 : Double the divisor and enter it with a blank on its right.Since 64 is the decimal part so put a decimal point in the quotient.
Step - 5 : We know 82 × 2 = 164, therefore, the new digit is 2. Divide and get the remainder.
Step - 6 : Since the remainder is 0 and no bar left, therefore 17.64 = 4.2 .
Students can also take the help of the online Square Root Calculator for solving problems on Square roots.