# ML Aggarwal Solutions Class 9 Mathematics Solutions for Rational and Irrational Numbers Exercise 1.4 in Chapter 1 - Rational and Irrational Numbers

Question 2 Rational and Irrational Numbers Exercise 1.4
1. Simplify the following:

(i) (5 + √7) (2 + √5)

(ii) (5 + √5) (5 - √5)

(v) (√2 + √3) (√5 + √7)

(vi) (4 + √5) (√3 - √7)

(i) (5 + √7) (2 + √5)

Let us simplify the expression,

= 5(2 + √5) + √7(2 + √5)

= 10 + 5√5 + 2√7 + √35

(ii) (5 + √5) (5 - √5)

Let us simplify the expression,

By using the formula,

(a)^{2}-(b)^{2} = (a + b) (a - b)

So,

=(5)^{2}-(\sqrt{5})^{2}

= 25 – 5

= 20

(iii) (\sqrt{5}+\sqrt{2})^{2}

Let us simplify the expression,

By using the formula, \begin{array}{l} (a+b)^{2}=a^{2}+b^{2}+2 a b \\ (\sqrt{5}+\sqrt{2})^{2}=(\sqrt{5})^{2}+(\sqrt{2})^{2}+2 \sqrt{5} \sqrt{2} \end{array}

= 3 + 7 - 2√21

= 10 - 2√21

(v) (√2 + √3) (√5 + √7)

Let us simplify the expression,

= √2(√5 + √7) + √3(√5 + √7)

= √2×√5 + √2×√7 + √3×√5 + √3×√7

= √10 + √14 + √15 + √21

(vi) (4 + √5) (√3 - √7)

Let us simplify the expression,

= 4(√3 - √7) + √5(√3 - √7)

= 4√3 - 4√7 + √15 - √35

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