How to find the common factors of squares

PSAT Math · Learn by Concept

Help Questions

PSAT Math › How to find the common factors of squares

1 - 3

1

Simplify the radical:

$\sqrt{320}$

$8\sqrt{5}$

CORRECT

$4\sqrt{20}$

0

$4\sqrt{5}$

0

$8\sqrt{20}$

0

$\sqrt{320}$

0

Explanation

$\sqrt{320}=\sqrt{2\times 160}=\sqrt{2\times 2\times 80}=2\sqrt{80}=2\sqrt{2\times 40}=2\sqrt{2\times 2\times 20}=2\times 2\times \sqrt{20}=4\sqrt{2\times 10}=4\sqrt{2\times 2\times 5}=4\times 2\times \sqrt{5}=8\sqrt{5}$

2

Solve for $\dpi{100} x$ :

$x\sqrt{45}+x\sqrt{72}=\sqrt{18}$

$x=\frac{\sqrt{2}}{\sqrt{5}+2\sqrt{2}}$

CORRECT

$x=\frac{\sqrt{2}}{\sqrt{5}}+\frac{1}{2}$

0

$x=\frac{\sqrt{5}}{\sqrt{2}}+2$

0

$x=\sqrt{9}$

0

$x=3$

0

Explanation

$x\sqrt{45}+x\sqrt{72}=\sqrt{18}$

Notice how all of the quantities in square roots are divisible by 9

$x\sqrt{9\times 5}+x\sqrt{9\times 8}=\sqrt{9\times 2}$

$x\sqrt{9}\sqrt{5}+x\sqrt{9}\sqrt{4\times 2}=\sqrt{9}\sqrt{2}$

$3x\sqrt{5}+3x\sqrt{4}\sqrt{2}=3\sqrt{2}$

$3x\sqrt{5}+6x\sqrt{2}=3\sqrt{2}$

$x(3\sqrt{5}+6\sqrt{2})=3\sqrt{2}$

$x=\frac{3\sqrt{2}}{3\sqrt{5}+6\sqrt{2}}$

Simplifying, this becomes

$x=\frac{\sqrt{2}}{\sqrt{5}+2\sqrt{2}}$

3

If m and n are postive integers and 4m = 2n, what is the value of m/n?

1/2

CORRECT

2

0

4

0

8

0

16

0

Explanation

22 = 4. Also, following the rules of exponents, 41 = 1.
One can therefore say that m = 1 and n = 2.
The question asks to solve for m/n. Since m = 1 and n = 2, m/n = 1/2.

Return to subject

AI Study CoachYour personal study buddy

Instant TutoringConnect with a tutor now

Request a TutorGet matched with an expert

Live ClassesJoin interactive classes

Question of the DayDaily practice to build your skills

FlashcardsStudy and memorize key concepts

WorksheetsBuild custom practice quizzes

AI SolverStep-by-step problem solutions

Learn by ConceptMaster concepts step by step

Diagnostic TestsAssess your knowledge level

Practice TestsTest your skills with exam questions

GamesLearn through free games