R S Aggarwal and Veena Aggarwal Solutions for Exercise 4: EXERCISE 1D

Examine whether the following numbers are rational or irrational:

$(5-\sqrt{5})(5+\sqrt{5})$

Examine whether the following numbers are rational or irrational:

$(\sqrt{3}+2{)}^2$

Examine whether the following numbers are rational or irrational:

$\frac{2\sqrt{13}}{3\sqrt{52}-4\sqrt{117}}$

Examine whether the following numbers are rational or irrational:

$\sqrt{8}+4\sqrt{32}-6\sqrt{2}$

On her birthday Reema distributed chocolates in an orphanage. The total number of chocolates she distributed is given by $(5+\sqrt{11})(5-\sqrt{11})$.

Find the number of chocolates distributed by her.

Simplifying $3\sqrt{45}-\sqrt{125}+\sqrt{200}-\sqrt{50}$ we get $4\sqrt{5}+5\sqrt{k}$. Find $k$

If we simplify $\frac{2\sqrt{30}}{\sqrt{6}}-\frac{3\sqrt{140}}{\sqrt{28}}+\frac{\sqrt{55}}{\sqrt{99}}$ we get $\frac{-x\sqrt{5}}{z}$. Find the value of $z$.

If we simplify $\sqrt{72}+\sqrt{800}-\sqrt{18}$ we get $a\sqrt{2}$. Find the value of $a$