Question

Which expression is equivalent to square root 128x^8y^3z^9? Assume y>0 and z>o

Answer 1

It is d because 64 x2 =128

Answer 2

Answer:

Option (3) is correct.

The given expression $\sqrt{128x^8y^3z^9}$  becomes $8x^4yz^4\sqrt{2yz}$

Step-by-step explanation:

Given : Expression $\sqrt{128x^8y^3z^9}$

We have to choose an equivalent expression to the given expression $\sqrt{128x^8y^3z^9}$ and choose the correct from the given options.

Consider the given expression  $\sqrt{128x^8y^3z^9}$

128 can be written as prime factors as 2 × 2 × 2 × 2 × 2 × 2 × 2 = $2^7$

Thus, $\sqrt{128}=\sqrt{2^7}=\sqrt{2^6\cdot 2}=2^3\sqrt{2}=8\sqrt{2}$

also, $\mathrm{Apply\:radical\:rule\:}\sqrt[n]{a^m}=a^{\frac{m}{n}},\:\quad \mathrm{\:assuming\:}a\ge 0$

$\sqrt{x^8}=x^{\frac{8}{2}}$

Similarly, $\sqrt{y^3}=\sqrt{y^2\cdot y}=y\sqrt{y}\\\\ \sqrt{z^8}=\sqrt{z^8\cdot z}=z^4\sqrt{z}$

Thus, The given expression $\sqrt{128x^8y^3z^9}$  becomes $8x^4yz^4\sqrt{2yz}$