[radical equations][section 63]
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(1.) √x
= 6 here is the problem
x = 36 square each side
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(2.) √x
- 9 = 8 here is the problem
x - 9 = 64 square each side
+
9 + 9 add 9 to each side
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x
= 73 add
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(3.) 3 + √x
- 1 = 5 here is the problem
-3 -3 subtract 3 from each side
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√x - 1 = 2
subtract
x - 1 = 4 square each side
+ 1 +
1 add 1 to each side
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x = 5 add
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(4.) 8 + 2√x = 0 here is the problem
-8 -8 subtract 8 from each side
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2√x
= -8 subtract
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2 2
divide each side by 2
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√x
= -4 divide and cancel
result: no solution
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(5.) 5√x
= 2 here is the problem
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5 5
divide each side by 5
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√x
= 2/5 cancel
x = 4/25 square each side
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(6.) 6 + √x = 13
here is the problem
-6 -6
subtract 6 from each side
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√x = 7
subtract
x = 49 square each side
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(7.) 8 = √5r
+ 1 here is the problem
64 = 5r + 1 square each side
-1 -1
subtract 1 from each side
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63 = 5r subtract
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5 5
divide each side by 5
12.6 = r divide and cancel
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(8.) √x2
+ 5 = x + 1 here is the
problem
x2 + 5 = x2
+ 2x + 1 square each side
-x2 -x2 subtract x2 from each side
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5 = 2x + 1 subtract
-1 -1 subtract 1 from each side
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4 = 2x subtract
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2 2 divide each side by 2
2 = x divide and cancel
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(9.) √x2
+ 24 = x + 12 here is the
problem
x2 + 24 = x2
+ 24x + 144 square each side
-x2 -x2 subtract x2 from each side
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24 = 24x + 144 subtract
24x + 144 = 24 just rearrange
-144 -144
subtract 144 from each side
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24x = -120 subtract
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24 24 divide each side by 24
x = -5 divide and cancel
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(10.) √3b2
- 5 = 11 here is the problem
3b2 - 5 = 121 square each side
+5 +5
add 5 to each side
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3b2 =
126 add
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3 3 divide each side by 3
b2 = 42 divide and cancel
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b = √42 b = -√42 take square roots