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3 years ago

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Which expression is equal to 728‾‾‾√−563‾‾‾√ ?

2 answers:

svet-max [94.6K]3 years ago

7 0

The answer is The 3rd one

marusya05 [52]3 years ago

7 0

Answer:

The correct option is 3.

Step-by-step explanation:

The given expression is

$7\sqrt{28}-5\sqrt{63}$

It can be written as

$7\sqrt{4\times 7}-5\sqrt{9\times 7}$

$7\sqrt{2^2\times 7}-5\sqrt{3^2\times 7}$

Using product property of radical expressions, we get

$7(\sqrt{2^2}\times \sqrt{7})-5(\sqrt{3^2}\times \sqrt{7})$ $[\because \sqrt{ab}=\sqrt{a}\sqrt{b}]$

$7(2\times \sqrt{7})-5(3\times \sqrt{7})$

$14\sqrt{7}-15\sqrt{7}$

Taking out common factors.

$\sqrt{7}(14-15)$

$\sqrt{7}(-1)$

$-\sqrt{7}$

Therefore the correct option is 3.

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3 years ago

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Which is the simplified form of the expression ((2 Superscript negative 2 Baseline) (3 Superscript 4 Baseline)) Superscript nega

AlekseyPX

Answer:

The option "StartFraction 1 Over 3 Superscript 8" is correct

That is $\frac{1}{3^8}$ is correct answer

Therefore $[(2^{-2})(3^4)]^{-3}\times [(2^{-3})(3^2)]^2=\frac{1}{3^8}$

Step-by-step explanation:

Given expression is ((2 Superscript negative 2 Baseline) (3 Superscript 4 Baseline)) Superscript negative 3 Baseline times ((2 Superscript negative 3 Baseline) (3 squared)) squared

The given expression can be written as

$[(2^{-2})(3^4)]^{-3}\times [(2^{-3})(3^2)]^2$

To find the simplified form of the given expression :

$[(2^{-2})(3^4)]^{-3}\times [(2^{-3})(3^2)]^2$

$=(2^{-2})^{-3}(3^4)^{-3}\times (2^{-3})^2(3^2)^2$ ( using the property $(ab)^m=a^m.b^m$ )

$=(2^6)(3^{-12})\times (2^{-6})(3^4)$ ( using the property $(a^m)^n=a^{mn}$

$=(2^6)(2^{-6})(3^{-12})(3^4)$ ( combining the like powers )

$=2^{6-6}3^{-12+4}$ ( using the property $a^m.a^n=a^{m+n}$ )

$=2^03^{-8}$

$=\frac{1}{3^8}$ ( using the property $a^{-m}=\frac{1}{a^m}$ )

Therefore $[(2^{-2})(3^4)]^{-3}\times [(2^{-3})(3^2)]^2=\frac{1}{3^8}$

Therefore option "StartFraction 1 Over 3 Superscript 8" is correct

That is $\frac{1}{3^8}$ is correct answer

6 0

3 years ago

Read 2 more answers