Question

asked Apr 27, 2020 150k views

2 Answers

Whozumommy · Answer 1 · 2020-04-28T18:00:36+0000

Answer:

The expression which is equivalent to the given expression is:

(√(5))/(x^2y)

We are given a expression as:

$\sqrt{(55x^7y^6)/(11x^(11)y^8)}$

Now we know that:

55=11* 5

Hence, we get:

$\sqrt{(55x^7y^6)/(11x^(11)y^8)}=\sqrt{(11* 5x^7y^6)/(11x^(11)y^8)$

which is written as:

$\sqrt{(5x^7y^6)/(x^(11)y^8)}$

Also, we know that if n>m

Then

(a^m)/(a^n)=(1)/(a^(n-m))

Hence, we have the expression as:

$=\sqrt{(5)/(x^(11-7)y^(8-6))}\\\\\\=\sqrt{(5)/(x^4y^2)$

This could be given as:

=(√(5))/(√(x^4)√(y^2))

Now, we know that:

$√(x^4)=√((x^2)^2)=x^2\\\\and\\\\√(y^2)=y$

Hence, we get that:

$\sqrt{(55x^7y^6)/(11x^(11)y^8)}=(√(5))/(x^2y)$

Max Wen · Answer 2 · 2020-05-03T08:32:14+0000

Answer:

(√(5) )/(x^(2) y)

Explanation:

That's a complex expression, let's simplify it, step by step, off the start, we'll simplify the 55/11:

$\sqrt{ (55 x^(7) y^(6) )/(11 x^(11) y^(8) ) } = \sqrt{ (5 x^(7) y^(6) )/(x^(11) y^(8) ) }$

Then we'll simplify the x's and y's:

$\sqrt{ (5 x^(7) y^(6) )/(x^(11) y^(8) ) } = \sqrt{ (5)/(x^(4) y^(2) ) }$

Let's split the square root in two and solve the bottom part:

$\sqrt{ (5)/(x^(4) y^(2) ) } = \frac{√(5) }{\sqrt{x^(4) y^(2)} } = (√(5) )/(x^(2) y)$

The solution is then:

(√(5) )/(x^(2) y)