Evaluate the expression -(49/64)^1/2

Mathematics

2 answers:

Nuetrik [128]3 years ago

8 0

The given expression is

$-(\frac{49}{64} )^{1/2}$

49 is the square of 7 and 64 is the square of 8.

So we can write the given expression as

$-(\frac{7^2}{8^2})^{1/2}$

$=-(\frac{7}{8})^{2*1/2} = -\frac{7}{8}$

Novosadov [1.4K]3 years ago

3 0

Rational expressions work like this: if you raise a number x to the power m/n, it means that you're considering the n-th root of x^m.

So, in this case, you are considering the second root (i.e. the square root) of 49/64 to the first power, i.e. 49/64 itself. In formula, you have

$\left(\cfrac{49}{64}\right)^{\frac{1}{2}} = \sqrt{\cfrac{49}{64}} = \cfrac{\sqrt{49}}{\sqrt{64}} = \cfrac{7}{8}$

Since there is a minus sign in front of the whole expression, the answer is -7/8

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ratio of pure lemon juice to water in the homestyle lemon drink is 5 : 19.

Step-by-step explanation:

In order to solve the final ratio of lemon juice to water, let us start by determining the initial ratio of pure lemon juice to water in the first mix. This is done as follows:

Total volume of mixture = 60 liters

initial volume of water = 60 liters

initial volume of lemon juice = 0 liters

1) She removed 15 liters of the water and replaced it with 15 liters of pure lemon juice.

Volume of water = 60 - 15 = 45 liters

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$\therefore \frac{15}{60}\ = \frac{1}{4}\ of\ the\ first\ mix\ is\ lemon\ juice\\\frac{45}{60}\ = \frac{3}{4}\ of\ the\ first\ mix\ is\ pure\ water$

2) She removed 10 liters of the new mixture

Let us convert this amount removed into ratio:

$lemon\ juice\ = \frac{1}{4}\ \times 10 = \frac{10}{4} = \frac{5}{2}\ liters.\\ \therefore the\ owner\ removes\ \frac{5}{2}\ liters\ of\ pure\ lemon\ juice\\pure\ water\ = \frac{3}{4}\ \times 10 = \frac{30}{4} = \frac{15}{2}\ liters\\ \therefore\ the\ owner\ removes\ \frac{15}{2}\ liters\ of\ water\ from\ the\ first\ mix.$

New volumes of water and lemon juice after removing the 10 liters of mixture is calculated as follows:

$lemon\ juice\ = 15 - \frac{5}{2} = \frac{30-5}{2} = \frac{25}{2}\ liters\ of\ lemon\ juice\\pure\ water\ = 45 - \frac{15}{2} = \frac{90-15}{2} = \frac{75}{2}\ liters\ of\ pure\ water$