Solve over the real numbers.
1) \(\sqrt{11x+5}=7\)
2) \(\sqrt{5x}-2=8\)
3) \(\sqrt{3x+2}=-5\)
4) \(\sqrt{3x+1}=\sqrt{5x-9}\)
5) \(3\sqrt[3]{8x-4}=18\)
6) \(\sqrt{20x+4}=x+5\)
7) \(\sqrt[3]{x-13}=\sqrt[3]{7x+8}\)
8) \(\frac{1}{2}\sqrt[3]{10x}-3=-1\)
9) \(\frac{\sqrt{14x+1}}{5}=3\)
10) \(\sqrt{x^2-26}=\sqrt{x-6}\)
11) \(\sqrt{24+x}=x+4\)
12) \(\sqrt{x}+4=\sqrt{x+40}\)
13) \(\sqrt{2x-4}+1=\sqrt{4x-15}\)
14) \(\sqrt{5x-14}=\sqrt{x-2}+2\)
15) \(2x^{\frac{2}{5}}=18\)
16) \(2x^{\frac{4}{3}}-5=27\)
17) \(-3(9x+4)^{\frac{3}{5}}=24\)
18) \((5x+1)^{\frac{3}{2}}-20=44\)
Review
Simplify the following expressions:
19) \(\sqrt[3]{6x^{14}y^{20}z^4} \cdot \sqrt[3]{12x^9y^{10}z^6}\)
20) \(\left(8x^9\right)^{\frac{1}{3}}\cdot \left(9x^5\right)^{\frac{1}{2}}\)
21) Convert \(y=2x^2-8x+5\) to vertex form, and then identify the vertex, domain, and range.
Solution Bank
1) \(\sqrt{11x+5}=7\)
2) \(\sqrt{5x}-2=8\)
3) \(\sqrt{3x+2}=-5\)
4) \(\sqrt{3x+1}=\sqrt{5x-9}\)
5) \(3\sqrt[3]{8x-4}=18\)
6) \(\sqrt{20x+4}=x+5\)
7) \(\sqrt[3]{x-13}=\sqrt[3]{7x+8}\)
8) \(\frac{1}{2}\sqrt[3]{10x}-3=-1\)
9) \(\frac{\sqrt{14x+1}}{5}=3\)
10) \(\sqrt{x^2-26}=\sqrt{x-6}\)
11) \(\sqrt{24+x}=x+4\)
12) \(\sqrt{x}+4=\sqrt{x+40}\)
13) \(\sqrt{2x-4}+1=\sqrt{4x-15}\)
14) \(\sqrt{5x-14}=\sqrt{x-2}+2\)
15) \(2x^{\frac{2}{5}}=18\)
16) \(2x^{\frac{4}{3}}-5=27\)
17) \(-3(9x+4)^{\frac{3}{5}}=24\)
18) \((5x+1)^{\frac{3}{2}}-20=44\)
Review
Simplify the following expressions:
19) \(\sqrt[3]{6x^{14}y^{20}z^4} \cdot \sqrt[3]{12x^9y^{10}z^6}\)
20) \(\left(8x^9\right)^{\frac{1}{3}}\cdot \left(9x^5\right)^{\frac{1}{2}}\)
21) Convert \(y=2x^2-8x+5\) to vertex form, and then identify the vertex, domain, and range.
Solution Bank