Question

Simplify the radical expression.

Answer 1

5. $\sqrt{250h^4k^5} = \sqrt{25 \times 10 (h^2)^2(k^2)^2k} = \sqrt{(5h^2k^2)^2\times 10k}=5h^2k^2\sqrt{10k}$

6. $\sqrt{14q} \times 2\sqrt{4q}=2 \sqrt{14q} \sqrt{4q}=2 \sqrt{14q4q} =2 \sqrt{14\times2^2q^2} =2\times2q \sqrt{14} = \\=4q \sqrt{14}$

7. $\sqrt{ \frac{63x^{15}y^9}{7xy^{11}}}= \sqrt{ \frac{9x^{14}}{y^2}}= \frac{3x^7}{y}$

8. $\sqrt{3} +4 \sqrt{3} =5 \sqrt{3}$

9. $2 \sqrt{6} +3 \sqrt{96}=2 \sqrt{6} +3 \sqrt{6\times16}= 2 \sqrt{6} +3 \times 4\sqrt{6}= \\= 2 \sqrt{6} +12\sqrt{6}= 14 \sqrt{6}$

10. $(8+ \sqrt{11} )(8- \sqrt{11} )=8^2- \sqrt{11} ^2=64-11=53$