Math / Numbers & Operations

QuestionSimplify $\sqrt{\frac{54}{96}}$

Studdy Solution

STEP 1

What is this asking? We need to simplify a square root of a fraction, making it as neat and tidy as possible! Watch out! Don't forget to simplify both the numerator and the denominator inside the square root first before tackling the square root itself.
It'll make things way easier!

STEP 2

1. Simplify the fraction inside the square root.
2. Simplify the square root.

STEP 3

Let's find the greatest common divisor (GCD) of 54 and 96.
We can do this by listing the factors of each number.
The factors of 54 are 1, 2, 3, 6, 9, 18, 27, and 54.
The factors of 96 are 1, 2, 3, 4, 6, 8, 12, 16, 24, 32, 48, and 96.
Looking at both lists, we see that the greatest common factor is 6.

STEP 4

Now, let's simplify our fraction by dividing both the numerator and the denominator by our GCD, 6. $\frac{54}{96} = \frac{54 \div 6}{96 \div 6} = \frac{9}{16}$ So, $\sqrt{\frac{54}{96}}$ becomes $\sqrt{\frac{9}{16}}$ .
Much better!

STEP 5

Remember, the square root of a fraction is the same as the square root of the numerator divided by the square root of the denominator.
Let's distribute that square root: $\sqrt{\frac{9}{16}} = \frac{\sqrt{9}}{\sqrt{16}}$

STEP 6

Now, let's calculate those square roots!
What number multiplied by itself gives us 9?
That's 3!
And what number multiplied by itself gives us 16?
That's 4! $\frac{\sqrt{9}}{\sqrt{16}} = \frac{3}{4}$

STEP 7

Our final simplified answer is $\frac{3}{4}$ !

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QuestionSimplify $\sqrt{\frac{54}{96}}$

Studdy Solution

STEP 1

What is this asking? We need to simplify a square root of a fraction, making it as neat and tidy as possible! Watch out! Don't forget to simplify both the numerator and the denominator inside the square root first before tackling the square root itself.
It'll make things way easier!

STEP 2

1. Simplify the fraction inside the square root.
2. Simplify the square root.

STEP 3

STEP 4

Now, let's simplify our fraction by dividing both the numerator and the denominator by our GCD, 6. $\frac{54}{96} = \frac{54 \div 6}{96 \div 6} = \frac{9}{16}$ So, $\sqrt{\frac{54}{96}}$ becomes $\sqrt{\frac{9}{16}}$ .
Much better!

STEP 5

Remember, the square root of a fraction is the same as the square root of the numerator divided by the square root of the denominator.
Let's distribute that square root: $\sqrt{\frac{9}{16}} = \frac{\sqrt{9}}{\sqrt{16}}$

STEP 6

Now, let's calculate those square roots!
What number multiplied by itself gives us 9?
That's 3!
And what number multiplied by itself gives us 16?
That's 4! $\frac{\sqrt{9}}{\sqrt{16}} = \frac{3}{4}$

STEP 7

Our final simplified answer is $\frac{3}{4}$ !

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QuestionSimplify 5496\sqrt{\frac{54}{96}}9654​​

Studdy Solution

STEP 1

What is this asking? We need to simplify a square root of a fraction, making it as neat and tidy as possible! Watch out! Don't forget to simplify both the numerator and the denominator *inside* the square root *first* before tackling the square root itself.It'll make things way easier!

STEP 2

1. Simplify the fraction inside the square root.2. Simplify the square root.

STEP 3

STEP 4

STEP 5

Remember, the square root of a fraction is the same as the square root of the numerator divided by the square root of the denominator.Let's **distribute** that square root: 916=916 \sqrt{\frac{9}{16}} = \frac{\sqrt{9}}{\sqrt{16}} 169​​=16​9​​

STEP 6

Now, let's **calculate** those square roots!What number multiplied by itself gives us **9**?That's **3**!And what number multiplied by itself gives us **16**?That's **4**! 916=34 \frac{\sqrt{9}}{\sqrt{16}} = \frac{3}{4} 16​9​​=43​

STEP 7

Our **final simplified answer** is 34\frac{3}{4}43​!

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Studdy solves anything!

Start learning now

Download Studdy AI Tutor now. Learn with ease and get all help you need to be successful at school.

QuestionSimplify $\sqrt{\frac{54}{96}}$

What is this asking? We need to simplify a square root of a fraction, making it as neat and tidy as possible! Watch out! Don't forget to simplify both the numerator and the denominator inside the square root first before tackling the square root itself.
It'll make things way easier!

1. Simplify the fraction inside the square root.
2. Simplify the square root.

Remember, the square root of a fraction is the same as the square root of the numerator divided by the square root of the denominator.
Let's distribute that square root: $\sqrt{\frac{9}{16}} = \frac{\sqrt{9}}{\sqrt{16}}$

Now, let's calculate those square roots!
What number multiplied by itself gives us 9?
That's 3!
And what number multiplied by itself gives us 16?
That's 4! $\frac{\sqrt{9}}{\sqrt{16}} = \frac{3}{4}$

Our final simplified answer is $\frac{3}{4}$ !