Disha Expert Team Solutions for Chapter: Square and Square Roots, Cube and Cube Roots, Indices and Surds, Exercise 1: Exercise

The largest number among $\sqrt{7}-\sqrt{5}, \sqrt{5}-\sqrt{3}, \sqrt{9}-\sqrt{7}, \sqrt{11}-\sqrt{9}$ is:

The value of ${\left[x^{\left(b-c\right)}\right]}^{b+c} {\left[x^{\left(c-a\right)}\right]}^{c+a} {\left[x^{\left(a-b\right)}\right]}^{a+b}$ is _____.

If $x^{\frac{1}{3}}+y^{\frac{1}{3}}=z^{\frac{1}{3}}$, then $\left\{{\left(x+y-z\right)}^3+27xyz\right\}$ will be equal to _____.

If $P=124,$ then $\sqrt[3]{P\left(P^2+3P+3\right)+1}=$?

If $a=2+\sqrt{3}$, then what is the value of $\left(a^2+a^{-2}\right)$?

If $p, q, r$ be integers such that $p^2=q^{2}r$, then:

What is the least number which must be subtracted from $369$ to make it a perfect cube?

Simplify the following expression: $\sqrt{\left\{\sqrt{4\sqrt{3\sqrt{6\sqrt{{25}^{72}}}}}\right\}\times \left\{\sqrt{2\sqrt{3\sqrt{4\sqrt{9^{48}}}}}\right\}}$