Answer:
Let x represent a number.
1.
[tex]2 \sqrt{x} = 12[/tex]
[tex] {}^{2} (2 \sqrt{x} = 12) {}^{2} [/tex]
[tex]2x = 144[/tex]
[tex] \frac{2x}{2} = \frac{144}{2} [/tex]
[tex]x = 72[/tex]
2.
[tex] \sqrt{x + 9} = 27[/tex]
[tex] {}^{2} ( \sqrt{x + 9} = 27) {}^{2} [/tex]
[tex]x + 9 = 729[/tex]
[tex]x = 729 - 9[/tex]
[tex]x = 720[/tex]
3.
[tex] \sqrt{2x + 3} = 6[/tex]
[tex] {}^{2} ( \sqrt{2x + 3} = 6) {}^{2} [/tex]
[tex]2x + 3 = 36[/tex]
[tex]2x = 36 - 3[/tex]
[tex]2x = 33[/tex]
[tex] \frac{2x}{2} = \frac{33}{2} [/tex]
[tex]x = 16.5[/tex]
4.
[tex]p = 4a[/tex]
[tex]25 = 4( \sqrt{x + 3} )[/tex]
[tex] {}^{2} (25 = 4\sqrt{x + 3} ) {}^{2} [/tex]
[tex]625 = 16(x + 3)[/tex]
[tex]625 = 16x + 48[/tex]
[tex]625 - 48 = 16x[/tex]
[tex]577 = 16x[/tex]
[tex] \frac{577}{16} = \frac{16x}{16} [/tex]
[tex]x = 36 \frac{1}{16} [/tex]
[tex]x = 36.0625[/tex]
5.
[tex]c = 2\pi \: r[/tex]
[tex]24 = 2(3.14)( \sqrt{x + 2} )[/tex]
[tex]24 = 6.28( \sqrt{x + 2} )[/tex]
[tex] {}^{2} (24 = 6.28( \sqrt{x + 2} )) {}^{2} [/tex]
[tex]576 = 39.4384(x + 2)[/tex]
[tex]576 = 39.4384x + 78.8768[/tex]
[tex]576 - 78.8768 = 39.4384x[/tex]
[tex]497.1232 = 39.4384x[/tex]
[tex] \frac{497.1232}{39.4384} = \frac{39.4384x}{39.4384} [/tex]
[tex]x = 12.6[/tex]
6.
[tex]a = {s}^{2} [/tex]
[tex]64m {}^{2} = {s}^{2} [/tex]
[tex] \sqrt{64m {}^{2} } = \sqrt{s {}^{2} } [/tex]
[tex]s = 8m[/tex]
8.
[tex]5 \sqrt{x} = 5[/tex]
[tex] {}^{2} (5 \sqrt{x} = 5) {}^{2} [/tex]
[tex]25x = 25[/tex]
[tex] \frac{25x}{25} = \frac{25}{25} [/tex]
[tex]x = 1[/tex]
9.
[tex] \sqrt[3]{x - 3} = 0[/tex]
[tex] {}^{3} ( \sqrt[3]{x - 3} = 0) {}^{3} [/tex]
[tex]x - 3 = 0[/tex]
[tex]x = 3[/tex]
10.
[tex] \sqrt{ \sqrt[3]{x} } = 2[/tex]
[tex] {}^{2} ( \sqrt{ \sqrt[3]{x} } = 2) {}^{2} [/tex]
[tex] \sqrt[3]{x} = 4[/tex]
[tex] {}^{3} ( \sqrt[3]{x} = 4) {}^{3} [/tex]
[tex]x = 64[/tex]
