Question

simplify :
$\sqrt[4]{16} - 8 \sqrt[3]{125} +15 \sqrt[5]{32} + \sqrt{576}$
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Answer 1

Question:

Simplify:

$\sqrt[4]{16} - 8 \sqrt[3]{125} +15 \sqrt[5]{32} + \sqrt{576}$

Solution:

$\sqrt[4]{16}= 2 \\ \sqrt[3]{125} = 5 \\ \sqrt[5]{32} = 2 \\ \sqrt{576} = 24$

Putting values

$\sqrt[4]{16} - 8 \sqrt[3]{125} +15 \sqrt[5]{32} + \sqrt{576}$

= 2 - 8(5) + 15(2) + 24

= 2 - 40 + 30 + 24

= 2 + 30 + 24 - 40

= 56 - 40

= 16

$\mathfrak{\large{\underline{\underline{Answer}}}}$

16

Answer 2

Answer:

$\sqrt[4]{16}-8\sqrt[3]{125}+15\sqrt[5]{32}+\sqrt{576}=16$

Step-by-step explanation:

$\sqrt[4]{16}-8\sqrt[3]{125}+15\sqrt[5]{32}+\sqrt{576}$

$\sqrt[4]{16}$

$\mathrm{Factor\:the\:number:\:}\:16=2^4$

$=\sqrt[4]{2^4}$

$\mathrm{Apply\:radical\:rule}:\quad \sqrt[n]{a^n}=a$

$\sqrt[4]{2^4}=2$

$=2$

$8\sqrt[3]{125}$

$\sqrt[3]{125}$

$\mathrm{Factor\:the\:number:\:}\:125=5^3$

$=\sqrt[3]{5^3}$

$\mathrm{Apply\:radical\:rule}:\quad \sqrt[n]{a^n}=a$

$=5$

$=8\cdot \:5$

$\mathrm{Multiply\:the\:numbers:}\:8\cdot \:5=40$

$=40$

$15\sqrt[5]{32}$

$\sqrt[5]{32}$

$\mathrm{Factor\:the\:number:\:}\:32=2^5$

$=\sqrt[5]{2^5}$

$\mathrm{Apply\:radical\:rule}:\quad \sqrt[n]{a^n}=a$

$\sqrt[5]{2^5}=2$

$=2$

$=15\cdot \:2$

$\mathrm{Multiply\:the\:numbers:}\:15\cdot \:2=30$

$=30$

$\sqrt{576}$

$\mathrm{Factor\:the\:number:\:}\:576=24^2$

$=\sqrt{24^2}$

$\mathrm{Apply\:radical\:rule}:\quad \sqrt[n]{a^n}=a$

$\sqrt{24^2}=24$

$=24$

$=2-40+30+24$

$\mathrm{Add/Subtract\:the\:numbers:}\:2-40+30+24=16$

$=16$