The square root of a given positive real number is another number which when multiplied with itself is the given number.

**Square
Root of Polynomials**

The square root of a given positive
real number is another number which when multiplied with itself is the given
number.

Similarly, the square
root of a given expression *p*(*x*) is another expression *q*(*x*)
which when multiplied by itself gives *p*(*x*), that is, *q* (*x*).
*q* ( *x* ) = *p*(*x*)

So, |*q* (*x*)|
= √*p*(*x*)*
*where* |q *(*x*)|* *is the absolute value of* q*(*x*).

The following two
methods are used to find the square root of a given expression

(i) Factorization method

(ii) Division method

1. Is *x* 2 + 4*x*
+ 4 a perfect square?

2. What is the value
of *x* in 3√*x* = 9 ?

3. The square root of
361*x* ^{4}*y*^{2} is _______.

4. √[ *a ^{2}x^{2} + 2abx + b^{2}*]
= _________

5. If a polynomial is
a perfect square then, its factors will be repeated number of times (odd
/ even)

Find the square root of
the following expressions

*Solution*

Find the square root of
the following expressions

(i) 16*x* ^{2}
+ 9*y* ^{2} − 24*xy* + 24*x* −18*y* + 9

(ii) (6*x* ^{2}
+ *x* −1)(3*x* ^{2} + 2*x* −1)(2*x* ^{2} +
3*x* + 1)

(iii) [√15*x*^{2} + (√3 + √10 ) *x*
+ √2][ √5*x*^{2} + (2√5 + 1)*x*+2][( √3*x*^{2} + (√2 + 2√3 ) *x*
+ 2√2]

Tags : Factorization Method, Example, Solution | Algebra , 10th Mathematics : Algebra

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10th Mathematics : Algebra : Square Root of Polynomials | Factorization Method, Example, Solution | Algebra

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