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Vlada [557]
3 years ago
10

An expression is shown below

Mathematics
1 answer:
Leno4ka [110]3 years ago
4 0

Answer:

B) It is irrational and equal to = 4\sqrt{2}

Step-by-step explanation:

The expression, \sqrt{18} + \sqrt{2} , is an irrational expression because it contains two irrational numbers, \sqrt{18} and \sqrt{2} . Both number are not perfect square. there is no whole number that would be squared that will give you 18 nor 2.

The expression can be equals the following:

\sqrt{18} + \sqrt{2}

= \sqrt{9*2} + \sqrt{2}

= \sqrt{9}*\sqrt{2} + \sqrt{2}

= 3\sqrt{2} + \sqrt{2}

= 4\sqrt{2}

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Option A

\left(y^{\frac{4}{3}} \cdot y^{\frac{2}{3}}\right)^{\frac{-1}{2}} = \left(y^{2}\right)^{\frac{-1}{2}}

<em><u>Solution:</u></em>

<em><u>Given expression is:</u></em>

\left(y^{\frac{4}{3}} \cdot y^{\frac{2}{3}}\right)^{\frac{-1}{2}}

<em><u>Product of powers property:</u></em>

The product of powers property tells us that when you multiply powers with the same base you just have to add the exponents

Which is represented as,

a^m.a^n = a^{m+n}

<em><u>Therefore, the given expression becomes,</u></em>

\left(y^{\frac{4}{3}+\frac{2}{3}}\right)^{\frac{-1}{2}}

Now add the exponents, we get

\left(y^{\frac{4+2}{3}}\right)^{\frac{-1}{2}}

Simplify the above expression

\left(y^{\frac{6}{3}}\right)^{\frac{-1}{2}}

Simplify the exponent of y, we get

\left(y^{2}\right)^{\frac{-1}{2}}

Thus Option A is correct

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Step-by-step explanation:

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