**Finding Square Root of Polynomial by Long Division Method Worksheet :**

Here we are going to see some practice questions on finding square root of the polynomial by long division method.

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

Here we are going to see how to find square root of a polynomial of degree 4.

(1) Find the square root of the following polynomials by division method

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

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

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

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

(2) Find the square root of the expression

(x^{2}/y^{2}) - 10x/y + 27 - (10y/x) + (y^{2}/x^{2})

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

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

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

(4) Find the values of m and n if the following expressions are perfect sqaures

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

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

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