Question

warm up 11/4/25

1. $4^2 =$
2. $5^2 =$
3. $8^2 =$
4. $sqrt{16} =$
5. $sqrt{36} =$
6. $sqrt{81} =$
7. if $x^2 = 100$, what is $x$?
8. if $x^2 = 50$, what is $x$?

Explanation:

Step1: Solve \(4^2\)

The exponent \(2\) means multiplying the base \(4\) by itself. So \(4^2 = 4\times4 = 16\).

Step2: Solve \(5^2\)

For \(5^2\), we multiply \(5\) by itself: \(5^2 = 5\times5 = 25\).

Step3: Solve \(8^2\)

Calculating \(8^2\), we do \(8\times8 = 64\).

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

The square root of a number is a value that, when squared, gives the original number. Since \(4^2 = 16\), \(\sqrt{16}=4\).

Step5: Solve \(\sqrt{36}\)

We know that \(6^2 = 36\), so \(\sqrt{36}=6\).

Step6: Solve \(\sqrt{81}\)

Because \(9^2 = 81\), \(\sqrt{81}=9\).

Step7: Solve \(x^2 = 100\) for \(x\)

To find \(x\) when \(x^2 = 100\), we take the square root of both sides. The square root of \(100\) is \(\pm10\) because \((10)^2 = 100\) and \((- 10)^2=100\), so \(x=\pm10\).

Step8: Solve \(x^2 = 50\) for \(x\)

Taking the square root of both sides, \(x=\pm\sqrt{50}\). Simplifying \(\sqrt{50}\), we can write \(50 = 25\times2\), so \(\sqrt{50}=\sqrt{25\times2}=5\sqrt{2}\). Thus, \(x = \pm5\sqrt{2}\).

Answer:

1. \(16\)
2. \(25\)
3. \(64\)
4. \(4\)
5. \(6\)
6. \(9\)
7. \(x=\pm10\)
8. \(x = \pm5\sqrt{2}\)