Question

Hello.

Please help with this maths problem:

`\mathrm{\displaystyle\frac{\sqrt{64xy^(5) } }{√(8x) } }`
Due today.
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Thank you in advance. :)

Answer 1

`\\ \rm\rightarrowtail (√(64xy^5))/(√(8x))`

`\\ \rm\rightarrowtail (√(8^2xy^5))/(√(8x))`

Follow the rule

`\boxed{\Large{\sf (a^m)/(a^n)=a^(m-n)}}`

`\\ \rm\rightarrowtail \sqrt{8^(2-1)x^(1-1)y^5}`

`\\ \rm\rightarrowtail √(8^1x^0y^5)`

• a^0=1
• a^1=a

`\\ \rm\rightarrowtail √(8y^5)`

`\\ \rm\rightarrowtail √(2^2(2)y^2y^3)`

`\\ \rm\rightarrowtail √(2^2y(y)(y)(y))`

`\\ \rm\rightarrowtail 2y^2√(2y)`

Answer 2

`\large{\boxed{\sf 2y^2√(2y)}}`

Explanation:

Here the given expression to us is ;

`\sf\qquad\longrightarrow (√(64xy^5))/(√(8x))`

Recall that ,

`\sf\qquad\longrightarrow (√(x))/(√(y))=\sqrt{(x)/(y)}`

On using this , we have ;

`\sf\qquad\longrightarrow \sqrt{\frac{\cancel{64}\cancel{x}y^5}{\cancel{8x}}}`

Simplify ,

`\sf\qquad\longrightarrow √( 8 y^5)`

The prime factorisation of 8 is 2³ . So ;

`\sf\qquad\longrightarrow √( (2^3)(y^5)) =√((2^2)(2)(y^2)(y^2)(y))`

Simplify the square root ,

`\sf\qquad\longrightarrow \pink{ 2y^2√(2y)}`

Hence the required answer is 2y²√{2y} .