How to find the common factors of squares - PSAT Math

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

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

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

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

x$\sqrt{9}$$\sqrt{5}$+x$\sqrt{9}$$\sqrt{4times 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{3sqrt{2}$}{3$\sqrt{5}$+6$\sqrt{2}$}

Simplifying, this becomes

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

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

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

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

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

x$\sqrt{9}$$\sqrt{5}$+x$\sqrt{9}$$\sqrt{4times 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{3sqrt{2}$}{3$\sqrt{5}$+6$\sqrt{2}$}

Simplifying, this becomes

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

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

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

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

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

x$\sqrt{9}$$\sqrt{5}$+x$\sqrt{9}$$\sqrt{4times 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{3sqrt{2}$}{3$\sqrt{5}$+6$\sqrt{2}$}

Simplifying, this becomes

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

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

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

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

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

x$\sqrt{9}$$\sqrt{5}$+x$\sqrt{9}$$\sqrt{4times 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{3sqrt{2}$}{3$\sqrt{5}$+6$\sqrt{2}$}

Simplifying, this becomes

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

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

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

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

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

x$\sqrt{9}$$\sqrt{5}$+x$\sqrt{9}$$\sqrt{4times 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{3sqrt{2}$}{3$\sqrt{5}$+6$\sqrt{2}$}

Simplifying, this becomes

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

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

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

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

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

x$\sqrt{9}$$\sqrt{5}$+x$\sqrt{9}$$\sqrt{4times 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{3sqrt{2}$}{3$\sqrt{5}$+6$\sqrt{2}$}

Simplifying, this becomes

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

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

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

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

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

x$\sqrt{9}$$\sqrt{5}$+x$\sqrt{9}$$\sqrt{4times 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{3sqrt{2}$}{3$\sqrt{5}$+6$\sqrt{2}$}

Simplifying, this becomes

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