Solve each of the following equations using the Extended Square Root Property.

Question

Solve each of the following equations using the Extended Square Root Property.

1. 8√x+7=16

x= _____________

2. √7x+4−3=0

x= _____________

3. 8√5x−7=16

x= _____________

Answer 1

Square Root Formula

The Square Root Formula is x² = c, which when solved for x becomes x = ±√c.

This formula represents the Square Root Property by solving as accurately for x as possible without another perfect square on the other side.

Using Properties of Equality

(√x)² = x

1. 8√x+7=16

8√x = 16- 7

8√x = 9

Squaring on both sides,

(8√x)² = 9²

64x = 81

x = 81/64

1. √7x+4−3=0

√7x = 3 -4

√7x = -1

Squaring on both sides,

(√7x)² = (-1)²

7x² = 1

x² = 1/7

x = +1/√7 or x = -1/√7

1. 8√5x−7=16

8√5x = 16+7

8√5x = 23

Squaring on both sides,

(8√5x)² = 23²

64*5*x² = 529

320x² = 529

x² = 529/320 or 23/8√5

x = + 23/8√5 or x = - 23/8√5