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8 problems match “radicals”. Clear

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1. Side length of a parallelogram from its area ●○○○○ 10 ptsA parallelogram has adjacent sides of lengths $s$ units and $2s$ units forming a $45^\circ$ angle. The area of the parallelogram is $8\sqrt{2}$ square units. Find the value of $s$. Round to two decimal places.
2. Sum of legs in a 30-60-90 triangle ●○○○○ 10 ptsA 30-60-90 right triangle has hypotenuse $2\sqrt{6}$ centimeters. Find the sum of the lengths, in centimeters, of its two legs. Round to two decimal places.
3. Side of a cube with volume 112 ●○○○○ 10 ptsThe volume of a cube is 112 cubic units. Find the length of each side. Round to two decimal places.
4. Radius of the wider can ●●○○○ 20 ptsTwo cylindrical cans have the same volume. The height of one can is triple the height of the other. If the radius of the narrower can is 12 units, find the radius of the wider can in units. Round to two decimal places.
5. Cube volume equals six times edge sum ●●○○○ 20 ptsThe volume of a cube is numerically equal to six times the sum of the lengths of its edges. Find the volume of the cube, in cubic units, rounded to two decimal places.
6. Limit of nested square roots ●●○○○ 20 ptsFind $\lim_{x\to\infty}\left(\sqrt{x+\sqrt{x+\sqrt{x}}}-\sqrt{x}\right)$.
7. Radical equation with cube roots ●●●○○ 50 ptsSolve the equation $\sqrt[3]{9-\sqrt{x+1}}+\sqrt[3]{7+\sqrt{x+1}}=4$.
8. Limit at root 6 with radicals ●●●○○ 50 ptsFind $\lim_{x\to\sqrt{6}}\frac{\sqrt{5+2x}-(\sqrt{3}+\sqrt{2})}{x^2-6}$. Round to two decimal places.