Radicals & Absolute Values - SAT Math
Card 0 of 29
Definition of a square root.
Definition of a square root.
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A number that, when multiplied by itself, equals the original number.
A number that, when multiplied by itself, equals the original number.
Domain of $f(x) = \sqrt{x - 5}$
Domain of $f(x) = \sqrt{x - 5}$
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$x \ge 5$.
$x \ge 5$.
Domain of $f(x) = \sqrt{x + 4}$.
Domain of $f(x) = \sqrt{x + 4}$.
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$x \ge -4$.
$x \ge -4$.
Explain why $\sqrt{-9}$ is not a real number.
Explain why $\sqrt{-9}$ is not a real number.
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No real number squared equals $-9$.
No real number squared equals $-9$.
For $y = -\sqrt{x}$, what happens to the graph?
For $y = -\sqrt{x}$, what happens to the graph?
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It reflects across the x-axis.
It reflects across the x-axis.
For $y = \sqrt{x - 4}$, what happens if 4 is increased?
For $y = \sqrt{x - 4}$, what happens if 4 is increased?
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Graph shifts right by 4.
Graph shifts right by 4.
For $y = 2\sqrt{x}$, what happens compared to $y = \sqrt{x}$?
For $y = 2\sqrt{x}$, what happens compared to $y = \sqrt{x}$?
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Graph is vertically stretched by factor of 2.
Graph is vertically stretched by factor of 2.
Given $f(x) = \sqrt{9 - x}$, what is the domain?
Given $f(x) = \sqrt{9 - x}$, what is the domain?
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$x \le 9$.
$x \le 9$.
Given $f(x) = \sqrt{x - 3}$, what is the domain?
Given $f(x) = \sqrt{x - 3}$, what is the domain?
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$x \ge 3$.
$x \ge 3$.
How does the absolute value of $a$ affect a parabola?
How does the absolute value of $a$ affect a parabola?
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Larger $|a|$ makes it narrower; smaller $|a|$ makes it wider.
Larger $|a|$ makes it narrower; smaller $|a|$ makes it wider.
If $f(x) = \sqrt{x - 1}$, what is the domain?
If $f(x) = \sqrt{x - 1}$, what is the domain?
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$x \ge 1$.
$x \ge 1$.
If $f(x) = \sqrt{x}$, what is $f(16)$?
If $f(x) = \sqrt{x}$, what is $f(16)$?
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4
4
Rationalize $\frac{3}{\sqrt{5}}$
Rationalize $\frac{3}{\sqrt{5}}$
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$\frac{3\sqrt{5}}{5}$.
$\frac{3\sqrt{5}}{5}$.
Simplify $(2\sqrt{3})(3\sqrt{2})$
Simplify $(2\sqrt{3})(3\sqrt{2})$
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$6\sqrt{6}$.
$6\sqrt{6}$.
Simplify $\sqrt[3]{27}$
Simplify $\sqrt[3]{27}$
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3
3
Simplify $\sqrt[3]{27}$.
Simplify $\sqrt[3]{27}$.
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3
3
Simplify $\sqrt{3x^2}$
Simplify $\sqrt{3x^2}$
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$|x|\sqrt{3}$.
$|x|\sqrt{3}$.
Simplify $\sqrt{49}$
Simplify $\sqrt{49}$
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7
7
Simplify $\sqrt{49}$.
Simplify $\sqrt{49}$.
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7
7
Simplify $\sqrt{50}$
Simplify $\sqrt{50}$
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$5\sqrt{2}$.
$5\sqrt{2}$.
Simplify $\sqrt{50}$.
Simplify $\sqrt{50}$.
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$5\sqrt{2}$.
$5\sqrt{2}$.
Simplify $\sqrt{72}$
Simplify $\sqrt{72}$
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$6\sqrt{2}$.
$6\sqrt{2}$.
Simplify $\sqrt{a^2}$
Simplify $\sqrt{a^2}$
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$|a|$.
$|a|$.
Simplify $\sqrt{x^4}$
Simplify $\sqrt{x^4}$
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$x^2$.
$x^2$.
Solve $\sqrt{x + 2} = x$
Solve $\sqrt{x + 2} = x$
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$x = 2$ (check eliminates $x = -1$).
$x = 2$ (check eliminates $x = -1$).
Solve $\sqrt{x} = 5$
Solve $\sqrt{x} = 5$
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$x = 25$.
$x = 25$.
Solve $\sqrt{x+3} = 4$
Solve $\sqrt{x+3} = 4$
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$x = 13$.
$x = 13$.
What is the definition of absolute value?
What is the definition of absolute value?
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Distance from 0 on a number line.
Distance from 0 on a number line.
Why must radical solutions be checked?
Why must radical solutions be checked?
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Squaring can introduce false solutions.
Squaring can introduce false solutions.