Question

find each square.

1. $8^2 = \square$ 2. $5^2 = \square$ 3. $6^2 = \square$ 4. $\left(\sqrt{16}\

ight)^2 = \square$

1. $\left(\sqrt{4}\

ight)^2 = \square$ 6. $10^2 = \square$ 7. $12^2 = \square$ 8. $15^2 = \square$

find the square root of each number

1. $\sqrt{64} = \square$ 10. $\sqrt{9} = \square$ 11. $\sqrt{36} = \square$ 12. $\sqrt{121} = \square$
2. $\sqrt{81} = \square$ 14. $\sqrt{100} = \square$ 15. $\sqrt{13^2} = \square$

Explanation:

Step1: Solve \(8^2\)

The square of a number \(a\) is \(a\times a\). So \(8^2 = 8\times8 = 64\).

Step2: Solve \(5^2\)

Using the definition of square, \(5^2 = 5\times5 = 25\).

Step3: Solve \(6^2\)

\(6^2 = 6\times6 = 36\).

Step4: Solve \((\sqrt{16})^2\)

First, \(\sqrt{16}=4\) (since \(4\times4 = 16\)), then \((\sqrt{16})^2=4^2 = 16\) (or by the property \((\sqrt{a})^2=a\) for \(a\geq0\), so \((\sqrt{16})^2 = 16\)).

Step5: Solve \((\sqrt{4})^2\)

Using the property \((\sqrt{a})^2=a\) (\(a\geq0\)), here \(a = 4\), so \((\sqrt{4})^2 = 4\) (or \(\sqrt{4}=2\), then \(2^2 = 4\)).

Step6: Solve \(10^2\)

\(10^2 = 10\times10 = 100\).

Step7: Solve \(12^2\)

\(12^2 = 12\times12 = 144\).

Step8: Solve \(15^2\)

\(15^2 = 15\times15 = 225\).

Step9: Solve \(\sqrt{64}\)

We need to find a number \(x\) such that \(x^2 = 64\). Since \(8\times8 = 64\), \(\sqrt{64}=8\).

Step10: Solve \(\sqrt{9}\)

Find \(x\) where \(x^2 = 9\). Since \(3\times3 = 9\), \(\sqrt{9}=3\).

Step11: Solve \(\sqrt{36}\)

Find \(x\) with \(x^2 = 36\). Since \(6\times6 = 36\), \(\sqrt{36}=6\).

Step12: Solve \(\sqrt{121}\)

Find \(x\) with \(x^2 = 121\). Since \(11\times11 = 121\), \(\sqrt{121}=11\).

Step13: Solve \(\sqrt{81}\)

Find \(x\) with \(x^2 = 81\). Since \(9\times9 = 81\), \(\sqrt{81}=9\).

Step14: Solve \(\sqrt{100}\)

Find \(x\) with \(x^2 = 100\). Since \(10\times10 = 100\), \(\sqrt{100}=10\).

Step15: Solve \(\sqrt{13^2}\)

Using the property \(\sqrt{a^2}=|a|\), for \(a = 13\) (positive), \(\sqrt{13^2}=13\).

Answer:

1. \(64\)
2. \(25\)
3. \(36\)
4. \(16\)
5. \(4\)
6. \(100\)
7. \(144\)
8. \(225\)
9. \(8\)
10. \(3\)
11. \(6\)
12. \(11\)
13. \(9\)
14. \(10\)
15. \(13\)