Question

3 + root 2 4 + root 7​

Answer 1

Answer:

Step-by-step explanation:3+root 24+root7

=3+2root6+root 7

Answer 2

3 + $\sqrt{24}$ + $\sqrt{7}$ = 3 + 2$\sqrt{6}$ + $\sqrt{7}$ or, $\sqrt{3}$($\sqrt{3}$ + 2$\sqrt{2}$) + $\sqrt{7}$

Step-by-step explanation:

3 + $\sqrt{24}$ + $\sqrt{7}$

To evaluate: 3 + $\sqrt{24}$ + $\sqrt{7}$ = ?

∴ 3 + $\sqrt{24}$ + $\sqrt{7}$

24 = 2 × 2 × 2 × 3

= 3 + $\sqrt{2\times 2\times 2 \times 3}$ + $\sqrt{7}$

= 3 + 2$\sqrt{2 \times 3}$ + $\sqrt{7}$

= 3 + 2$\sqrt{6}$ + $\sqrt{7}$

= $\sqrt{3}.\sqrt{3}$ + 2$\sqrt{2}.\sqrt{3}$  + $\sqrt{7}$ [ 3 = $\sqrt{3}.\sqrt{3}$ ]

= $\sqrt{3}$($\sqrt{3}$ + 2$\sqrt{2}$) + $\sqrt{7}$

∴ 3 + $\sqrt{24}$ + $\sqrt{7}$ = 3 + 2$\sqrt{6}$ + $\sqrt{7}$ or, $\sqrt{3}$($\sqrt{3}$ + 2$\sqrt{2}$) + $\sqrt{7}$