Mathematics, 12.01.2021 15:40 jonathon3957

Is $\sqrt{\frac{1}{4} } \\$ a rational number? Yes or No
is $\sqrt{ \\\\\\\frac{3}{16}$ a rational number?
Yes or no
Explain:

Answers: 2

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Answers

Answer from: candycrush24

Yes

Step-by-step explanation:

A rational number is a number that can be written in fraction form. Even the infinite decimal, if the infinite decimal can be written in a fraction form, we consider that as a rational number.

$\sqrt{ \frac{1}{4} }$

Any numbers that are inside the square root will be counted as irrational number. Unless if we are able to pull the number inside the square root all out.

From the square root, we are able to pull out 1 and 4.

$\sqrt{ \frac{1 \times 1}{2 \times 2} } \\ \frac{1}{2}$

Therefore, the square root of 1/4 is a rational number.

Next we have the square root of 3/16.

$\sqrt{ \frac{3}{16} }$

We can consider separately, for numerator and denominator.

For numerator which is 3, cannot be pulled out.

For denominator which is 4, can be evaluated as 2.

$\sqrt{ \frac{3}{2 \times 2} } \\ \frac{ \sqrt{3} }{2}$

The reason why I keep the evaluated square root of 2 as a denominator because of the properties.

$\sqrt{ \frac{x}{y} } = \frac{ \sqrt{x} }{ \sqrt{y} }$

So when we evaluate square root of 4 as a denominator, we will get 2 as a denominator.

Because there is still a square root which is square root of 3 and cannot be evaluated by pulling out.

Numbers inside Square Root are an approximately number. Unless can be evaluated by pulling the same two numbers.

Answer from: Quest

step-by-step explanation:

in standard form:

a= dictionaries

b= maps

you have to buy 3 dictionaries, so put a 3 next to the a (dictionaries) so that you can multiply them by each other.

a3+b= 60 (the amount of money you have)

we already know the cost of a=15 so replace a with $15

($15 x 3)+b=60

multiply 15 and 3 to get $45 and replace it with $45

45+b=60

and then replace b with 15 to get the total:

45+15=60

that means you have $15 left after buying 3 dictionaries.

15 divided by the cost of a map ($5) equals 3.

so you can buy 3 maps.

sorry if it was confusing!

Answer from: Quest

It's like discovering the answer to a puzzle. the purpose in solving an equation is to find the value or values of the variable that makes it a true statement. any value of the variable that makes the equation true is called a solution to the equation.