Question

Simplify: −√ − √+√ + −√2
please answer it​

Answer 1

Answer:

First, we factor 545454:

54=3\cdot 3\cdot 3\cdot 2=3^2\cdot 654=3⋅3⋅3⋅2=3

2

⋅654, equals, 3, dot, 3, dot, 3, dot, 2, equals, 3, squared, dot, 6

Then, we find the greatest perfect square in x^7x

7

x, start superscript, 7, end superscript:

x^7=\left(x^3\right)^2\cdot xx

7

=(x

3

)

2

⋅xx, start superscript, 7, end superscript, equals, left parenthesis, x, cubed, right parenthesis, squared, dot, x

And now we can simplify:

\begin{aligned} \sqrt{54x^7}&=\sqrt{3^2\cdot 6\cdot\left(x^3\right)^2\cdot x} \\\\ &=\sqrt{3^2}\cdot \sqrt6 \cdot\sqrt{\left(x^3\right)^2}\cdot \sqrt x \\\\ &=3\cdot\sqrt6\cdot x^3\cdot\sqrt x \\\\ &=3x^3\sqrt{6x} \end{aligned}

54x

7

=

3

2

⋅6⋅(x

3

)

2

⋅x

=

3

2

⋅

6

⋅

(x

3

)

2

⋅

x

=3⋅

6

⋅x

3

⋅

x

=3x

3

6x