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## Tamilnadu Samacheer Kalvi 10th Maths Solutions Chapter 3 Algebra Ex 3.8

**10th Maths Exercise 3.8 Samacheer Kalvi Question 1.**

Find the square root of the following polynomials by division method

(i) x^{4} – 12x^{3} + 42x^{2} – 36x + 9

(ii) 37x^{2} – 28x^{3} + 4x^{4} + 42x + 9

(iii) 16x^{4} + 8x^{2} + 1

(iv) 121x^{4} – 198x^{3} – 183x^{2} + 216x + 144

Solution:

The long division method in finding the square root of a polynomial is useful when the degrees of a polynomial is higher.

**Ex 3.8 Class 10 Samacheer Question 2.**

Find the square root of the expression \(\frac{x^{2}}{y^{2}}-10 \frac{x}{y}+27-10 \frac{y}{x}+\frac{y^{2}}{x^{2}}\)

Solution:

**10th Maths Exercise 3.8 Question 3.**

Find the values of a and b if the following polynomials are perfect squares

(i) 4x^{4} – 12x^{3} + 37x^{2} + bx + a

(ii) ax^{4} + bx^{3} + 361ax^{2} + 220x + 100

Solution:

(i)

Since it is a perfect square.

Remainder = 0

⇒ b + 42 = 0, a – 49 = 0

b = -42, a = 49

(ii) ax^{4} + bx^{3} + 361ax^{2} + 220x + 100

Since remainder is 0

a = 144

b = 264

**Exercise 3.8 Class 10 Samacheer Question 4.**

Find the values of m and n if the following expressions are perfect squares

(i) \(\frac{1}{x^{4}}-\frac{6}{x^{3}}+\frac{13}{x^{2}}+\frac{m}{x}+n\)

(ii) x^{4} – 8x^{3} + mx^{2} + nx + 16

Solution:

(i)

(ii)

Since remainder is 0,

m = 24, n = -32