Surds and Indices Questions for CAT

Find the value of $x$ if $2^x = 32$

Evaluate: $27^{-2/3}$

Simplify: $√49$

Determine the number of digits in the number $2401^{27}$ when expressed in base 7.

Simplify: $(2\sqrt{3})^2$

Simplify: $16^{1/2}$

Solve for $x$: $8^{2x+1} - 32^{x-1} = 2048$.

The real root of the equation $3^{4x} + 3^{2x+1} - 30 = 0$ is

What is the value of: $\sqrt{33 + 2\sqrt{33 + 2\sqrt{33 + \cdots}}}$

If $\sqrt{6x+8}+\sqrt{6x-8}=4(2+\sqrt{3})$, then $\sqrt{12x+8}$ equals

Simplify: $(\sqrt{3} + \sqrt{2})^2 - (\sqrt{3} - \sqrt{2})^2$

Simplify: $(\sqrt{3}+1)(\sqrt{3}-1)$

Find the value of $\sqrt{\ 33+2\sqrt{\ 33+2\sqrt{\ 33+....}}}$

Evaluate: $27^{-2/3}$

The sum of all real $k$ satisfying $\left(\tfrac{1}{25}\right)^k \cdot \left(\tfrac{1}{15625}\right)^{1/2} = \tfrac{1}{25}\cdot\left(\tfrac{1}{15625}\right)^{1/k}$ is:

The sum of all real values of $x$ satisfying the equation $2^{2x} - 6\cdot 2^{x} + 8 = 0$ is

What are the values of $x$ and $y$ that satisfy both the equations? (2006) $2^{0.7 x} \cdot 3^{-1.25 y}=8 \frac{\sqrt{6}}{27}$ $4^{0.3 x} \cdot 9^{0.2 y}=8 \cdot (81)^{1 / 5}$

Simplify: $9^{1/2} + 16^{1/4}$

Determine the sum of all possible x satisfying $5^{4x^2} - 5^{2x^2 + 2x + 12} + 5^{2x + 24} = 0$

If $(a+b\sqrt{m})$ is the positive square root of $(45-12\sqrt{11})$, where $a$ and $b$ are integers, and $m$ is a natural number, then the maximum possible value of $(a+b+m)$ is.