Find the square root of-i 4x2-20xy-25y2ii x6-1x6-2iii 6x2-x-2 3x2-5x-22x2-x-1

(i) √(4x^2+20xy+25y^2) = √((2x+5y)^2) =|2x+5y)| (ii) √(x^6+1x^6 2)= √( ( x^3 1x^3 )^2 ) = | ( x^3 1x^3 ) | (iii) First, let us factorize the polynom ...

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Byju's Answer

Standard X

Mathematics

Quadratic Formula

Find the squa...

Question

Find the square root of:
(i) $4 x^{2} + 20 x y + 25 y^{2}$
(ii) $x^{6} + \frac{1}{x^{6}} - 2$
(iii) $(6 x^{2} - x - 2) (3 x^{2} - 5 x + 2) (2 x^{2} - x - 1)$

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Solution

(i) $\sqrt{4 x^{2} + 20 x y + 25 y^{2}} = \sqrt{(2 x + 5 y)^{2}} = | 2 x + 5 y) |$

(ii) $\sqrt{x^{6} + \frac{1}{x^{6}} - 2} = \sqrt{{(x^{3} - \frac{1}{x^{3}})}^{2}} = ∣ ∣ ∣ (x^{3} - \frac{1}{x^{3}}) ∣ ∣ ∣$

(iii) First, let us factorize the polynomials
$6 x^{2} - x - 2 = (2 x + 1) (3 x - 2); 3 x^{2} - 5 x + 2 = (3 x - 2) (x - 1)$ and $2 x^{2} - x - 1 = (x - 1) (2 x + 1)$
Now, $\sqrt{(6 x^{2} - x - 2) (3 x^{2} - 5 x + 2) (2 x^{2} - x - 1)}$
$= \sqrt{(2 x + 1) (3 x - 2) \times (3 x - 2) (x - 1) \times (x - 1) (2 x + 1)}$
$\sqrt{(2 x + 1)^{2} (3 x - 2)^{2} (x - 1)^{2}} = | (2 x + 1) (3 x - 2) (x - 1) |$

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Find the square root of:(i) 4x2+20xy+25y2(ii) x6+1x6−2(iii) (6x2−x−2)(3x2−5x+2)(2x2−x−1)

Find the square root of:
(i) $4 x^{2} + 20 x y + 25 y^{2}$
(ii) $x^{6} + \frac{1}{x^{6}} - 2$
(iii) $(6 x^{2} - x - 2) (3 x^{2} - 5 x + 2) (2 x^{2} - x - 1)$