What is The Square Root of 64 over 49?

What is The Square Root of 64 over 49?

To find the square root of 64 over 49, you can take the square root of the numerator (64) and the square root of the denominator (49) separately:

√(64/49) = (√64) / (√49) = 8 / 7.

So, the square root of 64 over 49 simplifies to 8/7.

Simplifying a Fraction with Square Roots

Fractions containing square roots require simplifying the numerator and denominator separately before dividing. Strategically simplifying makes the fraction division process straightforward.

Let’s evaluate √64/49 by simplifying the square roots first.

Simplifying the Numerator

√64 The square root of 64 is 8, since 8×8 = 64

So √64 simplifies to 8.

Simplifying the Denominator

√49 The square root of 49 is 7, since 7×7 = 49

So √49 simplifies to 7.

Dividing the Simplified Fractions

With the simplified square roots, the fraction becomes:

8/7

No further simplification is needed, so:

√64/49 = 8/7

Understanding Why It Works

Simplifying the square roots separately maintains the part-to-whole relationship of the original fraction.

For example: √64/49 = square root of (64/49)

By ratio properties, the square root of a quotient is the quotient of the square roots.

Checking the Work

We can verify the simplified fraction 8/7 is correct by squaring it:

(8/7)2 = 64/49

Since squaring the simplified fraction gives the original, this confirms that √64/49 = 8/7 when fully simplified.

Simplifying fractions with square roots by evaluating the numerator and denominator separately makes the process clear and straightforward. This reinforces concepts like quotient rules and maintains the mathematical logic.

In summary, to simplify a fraction with square roots, first simplify the square root of the numerator and denominator separately, then divide the simplified fractions.