- Rational and Irrational Numbers
- Compound Interest
- Expansions
- Factorization
- Simultaneous Linear Equations
- Problems on Simultaneous Linear Equations
- Quadratic Equations
- Indices
- Logarithms
- Triangles
- Mid Point Theorem
- Pythagoras Theorem
- Rectilinear Figures
- Theorems on Area
- Circle
- Mensuration
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- Trigonometric Ratios and Standard Angles
- Coordinate Geometry
- Statistics
ML Aggarwal Solutions Class 9 Mathematics Solutions for Rational and Irrational Numbers Exercise 1.4 in Chapter 1 - Rational and Irrational Numbers
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- 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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