2.6 Other types of equations  (Page 5/10)

In a radical equation, what does it mean if a number is an extraneous solution?

Explain why possible solutions must be checked in radical equations.

Your friend tries to calculate the value $-9^{\frac{3}{2}}$ and keeps getting an ERROR message. What mistake is he or she probably making?

Explain why $\left|2x+5\right|=\mathrm{-7}$ has no solutions.

Explain how to change a rational exponent into the correct radical expression.

$x^{\frac{2}{3}}=16$

$x^{\frac{3}{4}}=27$

$2x^{\frac{1}{2}}-x^{\frac{1}{4}}=0$

${\left(x-1\right)}^{\frac{3}{4}}=8$

${\left(x+1\right)}^{\frac{2}{3}}=4$

$x^{\frac{2}{3}}-5x^{\frac{1}{3}}+6=0$

$x^{\frac{7}{3}}-3x^{\frac{4}{3}}-4x^{\frac{1}{3}}=0$

$x^3+2x^2-x-2=0$

$3x^3-6x^2-27x+54=0$

$4y^3-9y=0$

$x^3+3x^2-25x-75=0$

$m^3+m^2-m-1=0$

$2x^5\mathrm{-14}{x}^3=0$

$5x^3+45x=2x^2+18$

$\sqrt{3x-1}-2=0$

$\sqrt{x-7}=5$

$\sqrt{x-1}=x-7$

$\sqrt{3t+5}=7$

$\sqrt{t+1}+9=7$

$\sqrt{12-x}=x$

$\sqrt{2x+3}-\sqrt{x+2}=2$

$\sqrt{3x+7}+\sqrt{x+2}=1$

$\sqrt{2x+3}-\sqrt{x+1}=1$

$\left|3x-4\right|=8$

$\left|2x-3\right|=\mathrm{-2}$

$\left|1-4x\right|-1=5$

$\left|4x+1\right|-3=6$

$\left|2x-1\right|-7=\mathrm{-2}$

$\left|2x+1\right|-2=\mathrm{-3}$

$\left|x+5\right|=0$

$-\left|2x+1\right|=\mathrm{-3}$

$x^4-10x^2+9=0$

$4{\left(t-1\right)}^2-9\left(t-1\right)=\mathrm{-2}$

${\left(x^2-1\right)}^2+\left(x^2-1\right)-12=0$

${\left(x+1\right)}^2-8\left(x+1\right)-9=0$

${\left(x-3\right)}^2-4=0$

$x^{\mathrm{-2}}-x^{\mathrm{-1}}-12=0$

$\sqrt{{\left|x\right|}^2}=x$

$t^{10}-t^5+1=0$

$\left|x^2+2x-36\right|=12$

If the acceleration due to gravity is 9.8 m/s ² and the period equals 1 s, find the length to the nearest cm (100 cm = 1 m).

If the gravity is 32 ft/s ² and the period equals 1 s, find the length to the nearest in. (12 in. = 1 ft). Round your answer to the nearest in.

Find the height of a 72-kg female to the nearest cm whose $BSA=\mathrm{1.8.}$

Find the weight of a 177-cm male to the nearest kg whose $BSA=\mathrm{2.1.}$