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July 12, 2023
Go through the entire page to know important formulas for Surds and Indices to solve the questions of Surds and Indices quickly.
(an)m = (a)nmn√a = a(1/n)
Question 1 :
Find the value of (3x + 2y)^{2} using (a + b)^{2} formula.
Solution:
To find: The value of (3x + 2y)^{2}Let us assume that a = 3x and b = 2y.We will substitute these values in (a + b)^{2} formula:(a + b)^{2} = a^{2} + 2ab + b^{2}(3x + 2y)^{2} =(3x)^{2} + 2(3x)(2y) + (2y)^29x^{2} + 12xy + 4y^{2}
Answer:(3x + 2y)^{2} = 9x^{2} + 12xy + 4y^{2}
Question 2 :
Solve the following expression using suitable algebraic identity: (2x + 3y)^{3}
To find: (2x + 3y)^{3}Using (a + b)^{3}Formula,(a + b)^{3} = a^{3} + 3a2b + 3ab2 + b^{3}(2x)^{3} + 3 × (2x)2 × 3y + 3 × (2x) × (3y)2 + (3y)^{3}8x^{3} + 36x2y + 54xy2 + 27y^{3}
Answer: (2x + 3y)^{3} = 8x^{3} + 36x2y + 54xy2 + 27y^{3}
Question 3:
Rishi kapoor wants to know that by how much does \sqrt{12} + \sqrt{18} exceed \sqrt{3} + \sqrt{2} ?
Solution :
(\sqrt{12} + \sqrt{18}) – (\sqrt{3} + \sqrt{2} )(2\sqrt{3} – \sqrt{3}) – (3\sqrt{2} – \sqrt{2} )\sqrt{3} + 2\sqrt{2}
Question 4 :
Ranbeer kapoor wants to know the value of (256)^{0.16} \times (16)^{0.18} :
Expression = (256)^{0.16} \times (16)^{0.18} = (4)^{4}\times 0.16 \times (4)^{2}\times 0.18 = (4)^{0.64}\times (4)^{0.36} = (4)^{0.64+0.36} = (4)^{1} = 4
Question 5:
Sunil shetty wants to know that (0.04)^{–(1.5)} is equal to
Expression = (0.04)^{–1.5} = \frac{1}{ 0.04^{1.5}}
= \frac{1}{0.04^{\frac{3}{2}}} = \frac{1}{\sqrt{0. 0000064}} = \frac{1}{0.008} =\frac{1000}{8}= 125
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