y-7=y-1

To remove the radical on the left side of the equation, square both sides of the equation.

y-72=(y-1)2

Multiply the exponents in ((y-7)12)2.

Apply the power rule and multiply exponents, (am)n=amn.

(y-7)12⋅2=(y-1)2

Cancel the common factor of 2.

Cancel the common factor.

(y-7)12⋅2=(y-1)2

Rewrite the expression.

(y-7)1=(y-1)2

(y-7)1=(y-1)2

(y-7)1=(y-1)2

Simplify.

y-7=(y-1)2

y-7=(y-1)2

Simplify (y-1)2.

Rewrite (y-1)2 as (y-1)(y-1).

y-7=(y-1)(y-1)

Expand (y-1)(y-1) using the FOIL Method.

Apply the distributive property.

y-7=y(y-1)-1(y-1)

Apply the distributive property.

y-7=yy+y⋅-1-1(y-1)

Apply the distributive property.

y-7=yy+y⋅-1-1y-1⋅-1

y-7=yy+y⋅-1-1y-1⋅-1

Simplify and combine like terms.

Simplify each term.

Multiply yy.

Raise y to the power of 1.

y-7=y1y+y⋅-1-1y-1⋅-1

Raise y to the power of 1.

y-7=y1y1+y⋅-1-1y-1⋅-1

Use the power rule aman=am+n to combine exponents.

y-7=y1+1+y⋅-1-1y-1⋅-1

Add 1 and 1.

y-7=y2+y⋅-1-1y-1⋅-1

y-7=y2+y⋅-1-1y-1⋅-1

Rewrite y2 as y.

Use axn=axn to rewrite y as y12.

y-7=(y12)2+y⋅-1-1y-1⋅-1

Apply the power rule and multiply exponents, (am)n=amn.

y-7=y12⋅2+y⋅-1-1y-1⋅-1

Combine 12 and 2.

y-7=y22+y⋅-1-1y-1⋅-1

Cancel the common factor of 2.

Cancel the common factor.

y-7=y22+y⋅-1-1y-1⋅-1

Divide 1 by 1.

y-7=y1+y⋅-1-1y-1⋅-1

y-7=y1+y⋅-1-1y-1⋅-1

Simplify.

y-7=y+y⋅-1-1y-1⋅-1

y-7=y+y⋅-1-1y-1⋅-1

Move -1 to the left of y.

y-7=y-1⋅y-1y-1⋅-1

Rewrite -1y as -y.

y-7=y-y-1y-1⋅-1

Rewrite -1y as -y.

y-7=y-y-y-1⋅-1

Multiply -1 by -1.

y-7=y-y-y+1

y-7=y-y-y+1

Subtract y from -y.

y-7=y-2y+1

y-7=y-2y+1

y-7=y-2y+1

Since the radical is on the right side of the equation, switch the sides so it is on the left side of the equation.

y-2y+1=y-7

Move all terms not containing y to the right side of the equation.

Subtract y from both sides of the equation.

-2y+1=y-7-y

Subtract 1 from both sides of the equation.

-2y=y-7-y-1

Combine the opposite terms in y-7-y-1.

Subtract y from y.

-2y=0-7-1

Subtract 7 from 0.

-2y=-7-1

-2y=-7-1

Subtract 1 from -7.

-2y=-8

-2y=-8

Divide each term by -2 and simplify.

Divide each term in -2y=-8 by -2.

-2y-2=-8-2

Cancel the common factor of -2.

Cancel the common factor.

-2y-2=-8-2

Divide y by 1.

y=-8-2

y=-8-2

Divide -8 by -2.

y=4

y=4

To remove the radical on the left side of the equation, square both sides of the equation.

y2=42

Simplify each side of the equation.

Multiply the exponents in (y12)2.

Apply the power rule and multiply exponents, (am)n=amn.

y12⋅2=42

Cancel the common factor of 2.

Cancel the common factor.

y12⋅2=42

Rewrite the expression.

y1=42

y1=42

y1=42

Simplify.

y=42

Raise 4 to the power of 2.

y=16

y=16

y=16

Solve for y square root of y-7 = square root of y-1