Type roots, powers, and grouped fractions accurately

Use the root shortcut, then check what is inside

In SAT Desmos, type sqrt to open a square-root template. Enter the complete number or expression under the root, then use the right arrow to leave it before typing something outside the root.

Type nthroot for a root with an index. For a cube root, enter 3 in the small index and the number under the root. The index says how many equal factors reproduce that number: $\sqrt[3]{64}=4$ because $4\cdot 4\cdot 4=64$.

This simulator also uses a visual math editor: sqrt and nthroot create templates immediately. Use the arrow keys to position the cursor, and check which terms lie under each bar.

$\displaystyle \sqrt{81}$

Square root of 81: 9.

1. sqrt
2. 81
3. →

$\displaystyle \sqrt[3]{64}$

Cube root of 64: 4. Type nthroot, 3, right arrow, then 64.

1. nthroot
2. 3
3. →
4. 64

$\displaystyle 64^{\frac{1}{3}}$

Another way to enter the cube root of a positive number. Group the exponent.

Leave the exponent before continuing

Type ^ to enter a power. In the SAT calculator, the cursor enters the superscript. Press the right arrow to leave it before typing the next term. For $x^{2}+3$, the 3 must be on the main line.

Parentheses also distinguish $\left(-3\right)^{2}=9$ from $-3^{2}=-9$. The first squares the negative number; the second squares 3 and then negates it.

$\displaystyle x^{2}+3$

x squared, then add 3.

$\displaystyle 2^{x+1}$

The entire sum $x+1$ is the exponent.

Group the complete numerator and denominator

For a fraction divided by a fraction, type $\frac{1}{2}$, press the right arrow to leave it, then type / again. Type $\frac{3}{4}$ in the new denominator. The main fraction bar now separates $\frac{1}{2}$ from $\frac{3}{4}$, giving $\frac{2}{3}$.

The cursor determines what the next slash divides. A slash typed while you are still in a denominator nests another fraction there. Use the arrow keys and inspect the displayed grouping before continuing.

$\displaystyle \frac{\frac{1}{2}}{\frac{3}{4}}$

A fraction divided by a fraction: $\frac{2}{3}$.

1. 1/2
2. →
3. /
4. 3/4

$\displaystyle \frac{x+1}{x-2}$

The whole expression $x-2$ is the denominator. $x=2$ is excluded.

$\displaystyle \frac{1}{1+\frac{1}{2}}$

The whole denominator is 1 + $\frac{1}{2}$. Result: $\frac{2}{3}$.

Keep practicing the connected skills