Question

evaluate the square root.

\\\sqrt{0.64}\\

\\\sqrt{0.64} = \square\\ (type an integer or a decimal.)

Explanation:

🆕 New Concept Discovered: Evaluating Square Roots of Decimals
Finding what number multiplied by itself gives the decimal.

Step 1: Convert the decimal to a fraction

To make it easier to find the square root, we can rewrite the decimal \( 0.64 \) as a fraction. Since there are two decimal places, we place \( 64 \) over \( 100 \):

$$ 0.64 = \frac{64}{100} $$

So, the expression becomes:

$$ \sqrt{0.64} = \sqrt{\frac{64}{100}} $$

Step 2: Apply the quotient property of square roots

We can take the square root of the numerator and the denominator separately:

$$ \sqrt{\frac{64}{100}} = \frac{\sqrt{64}}{\sqrt{100}} $$

Step 3: Simplify the square roots

Find the numbers that multiply by themselves to give \( 64 \) and \( 100 \):

• Since \( 8 \times 8 = 64 \), we have \( \sqrt{64} = 8 \).
• Since \( 10 \times 10 = 100 \), we have \( \sqrt{100} = 10 \).

Substitute these values back into the fraction:

$$ \frac{\sqrt{64}}{\sqrt{100}} = \frac{8}{10} $$

Step 4: Convert back to a decimal

Convert the fraction \( \frac{8}{10} \) back into a decimal:

$$ \frac{8}{10} = 0.8 $$

Answer:

\( 0.8 \)