1] Twice the square root of a number is 12.
• Let the number be x
[tex]2 \sqrt{x} = 12[/tex]
[tex] \sqrt{x} = \frac{12}{2} [/tex]
[tex] \sqrt{x} = 6[/tex]
• Square both sides
[tex]( \sqrt{x})^{2} = {6}^{2} [/tex]
[tex]x = 36[/tex]
••••••••••••••••••••••••••••••••••••••••••••••••••
2] The square root of a number increased by 9 is 27.
• Let the number be x
[tex] \sqrt{x} + 9 = 27[/tex]
[tex] \sqrt{x} = 27 - 9[/tex]
[tex] \sqrt{x} = 18[/tex]
• Square both sides
[tex]( \sqrt{x})^{2} = {18}^{2} [/tex]
[tex]x = 324[/tex]
••••••••••••••••••••••••••••••••••••••••••••••••••
3] The square root of the sum of twice a number and 3 is 6.
• Let the number be x
[tex]\sqrt{2x + 3} = 6[/tex]
• Square both sides
[tex]( \sqrt{2x + 3})^{2} = {6}^{2} [/tex]
[tex]2x + 3 = 66[/tex]
[tex]2x = 36 - 3[/tex]
[tex]2x = 33[/tex]
[tex]x = \frac{33}{2} [/tex]
[tex]x = 16.5[/tex]
••••••••••••••••••••••••••••••••••••••••••••••••••
4] Five time the square root of a number is five.
• Let the number be x
[tex]5 \sqrt{x} = 5[/tex]
[tex] \sqrt{x} = \frac{5}{5} [/tex]
[tex] \sqrt{x} = 1[/tex]
• Square both sides
[tex]( \sqrt{x})^{2} = {1}^{2} [/tex]
[tex]x = 1[/tex]
••••••••••••••••••••••••••••••••••••••••••••••••••
5] Given:
Perimeter = 24 inch
Length = 4 inch
width = √x + 2 inch
•Perimeter = 2(Length + width)
[tex]24 = 2(4 + \sqrt{x + 2})[/tex]
[tex](4 + \sqrt{x + 2}) = \frac{24}{2} [/tex]
[tex](4 + \sqrt{x + 2}) = 12[/tex]
[tex] \sqrt{x + 2} = 12 - 4[/tex]
[tex] \sqrt{x + 2} = 8[/tex]
• Square both sides
[tex]( \sqrt{x + 2})^{2} = {8}^{2} [/tex]
[tex]x + 2 = 64[/tex]
[tex]x = 64 - 2[/tex]
[tex]x = 62[/tex]
[tex]\huge \color{red} \tt \largeﮩ٨ـﮩﮩ٨ـﮩﮩ Answer ﮩﮩـ٨ﮩﮩـ٨ﮩ[/tex]
1] The number is 36
2] The number is 324
3] The number is 16.5
4] The number is 1
5] x = 62
