Rational vs. Irrational
Is -0.625 rational or irrational?
Rational.
Fill in the blank with <, >, or =: √20 ___ 4.6.
√20 < 4.6
Between which two consecutive integers does √37 lie on a number line?
6 and 7
Which number is irrational: √169, √45, or √(25/49)?
√45
Which is greater: √58 or 15/2?
√58 is greater.
On a number line, is √27 closer to 5 or 6? Explain using an estimate.
Closer to 5.
Sort these numbers into rational and irrational: 0.272727..., -√81, π + 2, √63.
Rational: 0.272727... = 3/11 and -√81 = -9. Irrational: π + 2 and √63.
Order from least to greatest: √7, 2.75, 8/3, 2.6.
2.6, √7, 8/3, 2.75.
Estimate √61 to the nearest tenth. Where would you place it on a number line?
At about 7.8
Is 5/6 - 2√7 rational or irrational? Explain your reasoning.
Irrational.
Order from least to greatest: √17, 4.1, 21/5, 4.05, √18.
4.05, 4.1, √17, 21/5, √18.
Four points on a number line are A = -8.8, B = -8.2, C = -7.7, and D = -7.1. Which point is closest to -√68?
Point B.
A student says √48 - 4√3 is irrational because both terms are irrational. Is the student correct? And why?
No. √48 = 4√3, so √48 - 4√3 = 0. Zero is rational.
Order from greatest to least: -√13, -3.5, -11/3, -√12.
-√12, -3.5, -√13, -11/3 .
A number line has A = 2.4, B = 3.6, C = 4.4, and D = 4.8.
Match each radical to its closest point: √23, √6, √19, √13.
√23 → D; √6 → A; √19 → C; √13 → B.