Solving Radical Equations - Examples & Practice
Read this topicExplanations 3
- A radical is any expression that uses some form of the 0\sqrt{\phantom{0}}0 sign. The radical you'll probably see most is the square root, but you could also see cube root (03\…
By Hannah Bonville, Alex Federspiel, Joshua Siktar, Amy Feraco, Jonathan Heller, Anusha Rahman
- (Videos) Solving Radical Equations by mathman1024 This video by mathman1024 works through equations with one radical. Summary\large{\text{Summary}}Summary The power property sta…
By Alex Federspiel, Amy Feraco, Jonathan Heller, Anusha Rahman
- Equations with a Single Radical Radicals come in different forms. Some are square roots, some are cube roots, and so on. Luckily, when you are solving an equation with a single …
By Caroline K
Problems 28
- Solve for xxx. 3x−6−6=6\sqrt{3x-6}-6=63x−6−6=6
- Solve for xxx. x−8−6=1\sqrt{x-8}-6=1x−8−6=1
- Solve for xxx. x+5−18=−15\sqrt{x+5}-18=-15x+5−18=−15
- Solve for xxx. 3x+7−1=0\sqrt{3x+7}-1=03x+7−1=0
- Solve for xxx. −10x−2+27=33\sqrt{-10x-2}+27=33−10x−2+27=33
- Solve for xxx. 9x−9−10=5\sqrt{9x-9}-10=59x−9−10=5
- The distance formula is d=(x2−x1)2+(y2−y1)2d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}d=(x2−x1)2+(y2−y1)2. Solve for y1y_1y1.
- The surface area of a cone can be found using the following equation. SA=πrr2+h2S_A=\pi r\sqrt{r^2+h^2}SA=πrr2+h2 Solve for hhh.
- The distance between two points is given by the formula d=(x2−x1)2+(y2−y1)2.d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}.d=(x2−x1)2+(y2−y1)2. If you know the distance between two point…
- Find all real numbers such that x≥0x\ge0x≥0 and x<4x\sqrt x < 4xx<4x.
- The bases of a trapezoid have lengths 101010 and 212121, and the legs have lengths 34\sqrt{34}34 and 353 \sqrt{5}35. What is the area of the trapezoid? Express your answer as …
- Solve for the value of xxx in the equation (x2)−19+13=17\sqrt{\left(\frac{x}{2}\right)-19}+13=17(2x)−19+13=17.
- Solve for xxx in terms of yyy: y=x+1y=\sqrt{x+1}y=x+1
- Solve for xxx: 2x=4\sqrt{2x}=42x=4
- Solve for xxx: x2=3\sqrt{\frac{x}{2}}=32x=3
- Solve for xxx in terms of yyy: 4y=2x+2y4y=\sqrt{2x+2y}4y=2x+2y
- Polly wants to purchase a cover for her circular swimming pool, so she needs to find the size of cover that she needs. From one side to the other through the middle of the pool,…
- Solve for xxx: 2x3=2\sqrt[3]{2x}=232x=2
- 8x2=1\sqrt{8x^2}=18x2=1 Solve for xxx, given that x>0x>0x>0.
- Solve for the possible real value(s) of xxx. 25x4=20\sqrt{25x^4}=2025x4=20
- 4x6=16\sqrt{4x^6}=164x6=16 Solve for xxx, given that x>0x>0x>0.
- Find xxx such that 5=x−4.5=\sqrt{x}-4.5=x−4.
- Find the unique value of xxx such that x−23−1=1.\sqrt[3]{x-2}-1=1.3x−2−1=1.
- Find all real values of xxx such that x2=x.x^2=\sqrt{x}.x2=x.
- Fill in the box with a real number so that ?+5=3.\sqrt{\boxed{?}} + 5 = 3.?+5=3.
- Fill in the box with a real number so that ?+3=5.\sqrt{\boxed{?}} + 3 = 5.?+3=5.
- When might the first possibility (divide by bbb) be a better first step than the second?
- Which of the following are solutions to the equation x−5x+7=−11?x - 5\sqrt{x + 7} = -11?x−5x+7=−11?