Rational, Irrational, and Estimation
Determine which consecutive integers the square root is between.
\sqrt(12)
3 and 4
Simplify completely. Leave answers in simplified radical form.
\sqrt(25)
5
Perform the indicated operations and simplify completely. Leave answers in simplified radical form.
5\sqrt(6)+15\sqrt(6)
20\sqrt(6)
Perform the indicated operations and simplify completely. Leave answers in simplified radical form.
\sqrt(3)\sqrt(12)
6
Perform the indicated operations and simplify completely. Leave answers in simplified radical form.
\frac(3)(5)
Determine if the following number is rational or irrational.
4
Rational
Simplify completely. Leave answers in simplified radical form.
3*\sqrt(16)
12
Perform the indicated operations and simplify completely. Leave answers in simplified radical form.
8\sqrt(x)+\sqrt(x)
9\sqrt(x)
Perform the indicated operations and simplify completely. Leave answers in simplified radical form.
4\sqrt(32)
16\sqrt(2)
Perform the indicated operations and simplify completely. Leave answers in simplified radical form.
\frac(\sqrt(75))(\sqrt(25))
\sqrt(3)
Determine if the following number is rational or irrational.
\sqrt(45)
Irrational
Simplify completely. Leave answers in simplified radical form.
2(8\sqrt(64))
128
Perform the indicated operations and simplify completely. Leave answers in simplified radical form.
\sqrt(50)-10\sqrt(2)
-5\sqrt(2)
Perform the indicated operations and simplify completely. Leave answers in simplified radical form.
\sqrt(6)(7\sqrt(6))
42
Perform the indicated operations and simplify completely. Leave answers in simplified radical form.
\sqrt(\frac(4)(64))
1/4
Determine if the following number is rational or irrational.
\frac(3)(4)
Rational
Simplify completely. Leave answers in simplified radical form.
\sqrt(72)
6\sqrt2
Perform the indicated operations and simplify completely. Leave answers in simplified radical form.
3\sqrt(54)-9\sqrt(6)
0
Perform the indicated operations and simplify completely. Leave answers in simplified radical form.
4x\sqrt3
Rationalize the denominator and simplify completely.
\frac(3)(\sqrt(6))
\frac(\sqrt(6))(2)
Determine the consecutive integers the square root is between.
\sqrt(212)
14 and 15
Simplify completely. Leave answers in simplified radical form.
5\sqrt(48x^2)
20x\sqrt3
Perform the indicated operations and simplify completely. Leave answers in simplified radical form.
2\sqrt(32)+5\sqrt(50)
33\sqrt(2)
Perform the indicated operations and simplify completely. Leave answers in simplified radical form.
2\sqrt(24)(5\sqrt(12))
120\sqrt(2)
Rationalize the denominator and simplify completely.
\frac(4\sqrt(2))(\sqrt(5))
\frac(4\sqrt(10))(5)