Root Search Worksheet
Root Search Worksheet
Solving Radical Equations: Lab Notes
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Laboratory Instructions
Analyze the radical functions below. For each problem, determine the value of x that satisfies the given output. Show all algebraic steps (squaring both sides, isolating the variable) to justify your findings.
01
Given \( g(x) = \sqrt{2(x-3)} \), determine the value of \( x \) when \( g(x) = 4 \).
02
Given \( h(x) = \sqrt{5(x+4)} \), determine the value of \( x \) when \( h(x) = 5 \).
03
Given \( f(x) = \sqrt{2(x-2)} \), determine the value of \( x \) when \( f(x) = 6 \).
04
Given \( j(x) = \sqrt{8(x+1)} \), determine the value of \( x \) when \( j(x) = 8 \).
05
Given \( k(x) = \sqrt{2x+4} \), determine the value of \( x \) when \( k(x) = 6 \).
06
Given \( m(x) = \sqrt{3x-6} \), determine the value of \( x \) when \( m(x) = 3 \).
07
Given \( p(x) = \sqrt{4(x+2)} \), determine the value of \( x \) when \( p(x) = 10 \).
08
Given \( q(x) = \sqrt{2(x+7)} \), determine the value of \( x \) when \( q(x) = 4 \).
09
Given \( r(x) = \sqrt{6(x+2)} \), determine the value of \( x \) when \( r(x) = 6 \).
10
Given \( s(x) = \sqrt{3(x-1)} \), determine the value of \( x \) when \( s(x) = 9 \).
Root Search Answer Key
Root Search Answer Key
Validated Laboratory Results
Teacher Resource
Algebraic Verification
All solutions follow the standard procedure: 1) Square both sides, 2) Divide by the leading coefficient (if applicable), 3) Solve for x.
01 SOLUTION
\( g(x) = 4 \)
\( 4 = \sqrt{2(x-3)} \)
\( 16 = 2(x-3) \)
\( 8 = x - 3 \)
\( x = 11 \)
02 SOLUTION
\( h(x) = 5 \)
\( 5 = \sqrt{5(x+4)} \)
\( 25 = 5(x+4) \)
\( 5 = x + 4 \)
\( x = 1 \)
03 SOLUTION
\( f(x) = 6 \)
\( 6 = \sqrt{2(x-2)} \)
\( 36 = 2(x-2) \)
\( 18 = x - 2 \)
\( x = 20 \)
04 SOLUTION
\( j(x) = 8 \)
\( 8 = \sqrt{8(x+1)} \)
\( 64 = 8(x+1) \)
\( 8 = x + 1 \)
\( x = 7 \)
05 SOLUTION
\( k(x) = 6 \)
\( 6 = \sqrt{2x+4} \)
\( 36 = 2x + 4 \)
\( 32 = 2x \)
\( x = 16 \)
06 SOLUTION
\( m(x) = 3 \)
\( 3 = \sqrt{3x-6} \)
\( 9 = 3x - 6 \)
\( 15 = 3x \)
\( x = 5 \)
07 SOLUTION
\( p(x) = 10 \)
\( 10 = \sqrt{4(x+2)} \)
\( 100 = 4(x+2) \)
\( 25 = x + 2 \)
\( x = 23 \)
08 SOLUTION
\( q(x) = 4 \)
\( 4 = \sqrt{2(x+7)} \)
\( 16 = 2(x+7) \)
\( 8 = x + 7 \)
\( x = 1 \)
09 SOLUTION
\( r(x) = 6 \)
\( 6 = \sqrt{6(x+2)} \)
\( 36 = 6(x+2) \)
\( 6 = x + 2 \)
\( x = 4 \)
10 SOLUTION
\( s(x) = 9 \)
\( 9 = \sqrt{3(x-1)} \)
\( 81 = 3(x-1) \)
\( 27 = x - 1 \)
\( x = 28 \)
