PE 1 - Surds & Indices | Algebra - Surds & Indices

Simplify: $\sqrt{\sqrt[3]{\sqrt[4]{\sqrt[5]{\sqrt[6]{8^{240}}}}}}$

• (a)

  2

• (b)

  64

• (c)

  8

• (d)

  None of these

• Solution
• Discuss
• Report

Find the value of $\sqrt{\frac{\sqrt{a+b}+\sqrt{a-b}}{\sqrt{a+b}-\sqrt{a-b}}}$, where a = 2 and b = 1.

• (a) $\frac{\sqrt{3}-1}{\sqrt{2}}$
• (b) $\frac{\sqrt{3}+1}{\sqrt{2}}$
• (c) $\frac{\sqrt{2}+1}{\sqrt{3}}$
• (d)

  None of these

• Solution
• Discuss
• Report

Find the value of $\sqrt[ab]{x^{c^2}}\times \sqrt[bc]{x^{a^2}}\times \sqrt[ca]{{x^b}^2}$& if a + b + c = 0.

• (a)

  x³

• (b)

  x

• (c)

  x²

• (d)

  x^abc

• Solution
• Discuss
• Report

If x = 3 + $\sqrt[3]{3}$ + $\sqrt[3]{9}$, then find the value of x³ - 18x² + 18x + 27?

• (a)

  √108

• (b)

  8

• (c)

  √66

• (d)

  66

• (e)

  None of these

• Solution
• Discuss
• Report

If 3^x + 5^y = 52 and 3^2x-2 + 5^y+1 = 206 where x and y are integers, find x + y.

• (a)

  3

• (b)

  4

• (c)

  5

• (d)

  6

• (e)

  Cannot be determined

• Solution
• Discuss
• Report

If x is a positive integer, the greatest integer by which 11^x + 11^x+1 + 11^x+2 is always divisible is

• (a)

  11

• (b)

  121

• (c)

  133

• (d)

  1463

• Solution
• Discuss
• Report

Find square root of 5 + √6 + √10 + √15.

• (a)

  √2 + √3 + √5

• (b)

  1 + $\sqrt{\frac{3}{2}}$ + $\sqrt{\frac{5}{2}}$

• (c)

  (√2 + √3 + √5)/2

• (d)

  None of these

• Solution
• Discuss
• Report

Given 2^x = 8^y+1 and 9^y = 3^x–9; the value of x + y  is:

• (a)

  18

• (b)

  21

• (c)

  24

• (d)

  27

• Solution
• Discuss
• Report

Let r be the result of doubling both the base and the exponent of a^b, b ≠ 0. If r equals the product of a^b and x^b, then x equals:

• (a)

  2a

• (b)

  4a

• (c)

  2

• (d)

  4

• Solution
• Discuss
• Report

The expression $\sqrt{\frac{4}{3}}-\sqrt{\frac{3}{4}}$ is equal to:
 

• (a)

  $\frac{\sqrt{3}}{6}$

• (b)

  -$\frac{\sqrt{3}}{6}$

• (c)

  $\frac{\sqrt{-3}}{6}$

• (d)

  5$\frac{\sqrt{3}}{6}$

• Solution
• Discuss
• Report