Question

express 5√5 as the square root of a single number show your work

Answer 1

To express \( 5\sqrt{5} \) as the square root of a single number, we can follow these steps:

1. Start with the expression \( 5\sqrt{5} \).
2. Rewrite \( 5 \) in terms of a square root. Since \( 5 = \sqrt{5^2} \) or \( 5 = \sqrt{25} \), we have:
\[
5\sqrt{5} = \sqrt{25} \cdot \sqrt{5}
\]
3. Use the property of square roots that states \( \sqrt{a} \cdot \sqrt{b} = \sqrt{a \cdot b} \):
\[
\sqrt{25} \cdot \sqrt{5} = \sqrt{25 \cdot 5}
\]
4. Now, calculate \( 25 \cdot 5 \):
\[
25 \cdot 5 = 125
\]
5. Therefore, we can express \( 5\sqrt{5} \) as:
\[
5\sqrt{5} = \sqrt{125}
\]

In conclusion, \( 5\sqrt{5} \) can be expressed as the square root of a single number:
\[
5\sqrt{5} = \sqrt{125}
\]

Answer 2

EXPAND AND SIMPLIFY (3-2√7)²

Answer 3

To expand and simplify \((3 - 2\sqrt{7})^2\), we can use the formula for the square of a binomial:

\[
(a - b)^2 = a^2 - 2ab + b^2
\]

In our case, \(a = 3\) and \(b = 2\sqrt{7}\). Now we can apply the formula:

1. First, calculate \(a^2\):
\[
a^2 = 3^2 = 9
\]

2. Next, calculate \(2ab\):
\[
2ab = 2 \cdot 3 \cdot (2\sqrt{7}) = 12\sqrt{7}
\]

3. Now, calculate \(b^2\):
\[
b^2 = (2\sqrt{7})^2 = 4 \cdot 7 = 28
\]

Now substitute these values into the formula:

\[
(3 - 2\sqrt{7})^2 = a^2 - 2ab + b^2 = 9 - 12\sqrt{7} + 28
\]

4. Combine like terms:

\[
9 + 28 = 37
\]

Therefore, we have:

\[
(3 - 2\sqrt{7})^2 = 37 - 12\sqrt{7}
\]

So the expanded and simplified form of \((3 - 2\sqrt{7})^2\) is:

\[
\boxed{37 - 12\sqrt{7}}
\]