Square root — Grade 7 Math, what it means and where it is taught
For k ≥ 0, √k is the nonnegative number whose square is k.
Taught in Grade 7 Math.
Where it is taught
What uses it later
This idea is needed for:
- Index — The little number on the root. Square root has index 2, cube root index 3.
- Domain restriction — A square root needs its inside to be ≥ 0, which limits the inputs allowed.
Practise this idea
14 questions in the course bank use Square root, in Proportional Reasoning with Scale Drawings, Squares & Square Roots, Real Numbers, Dilations & Similarity, Distance on the Coordinate Plane, Solving Quadratic Equations. The first 8 are below; the rest are in those units.
Problem 1
Two similar figures have areas 25 cm2 and 64 cm2. The smaller has perimeter 20 cm. Find the larger perimeter.
Worked answer
32
k2 = 6425, so k = 85
Perimeter is a length, so it scales by k
20 × 85 = 32 cm
Problem 2
A square has area 169 cm2. Find its side length.
Worked answer
13
√169 = 13 cm
Problem 3
Which of these is irrational?
- 0.25
- 23
- √16
- √11
Worked answer
√11
0.25 and 23 are fractions, so rational
√16 = 4, rational
11 is not a perfect square, so √11 is irrational.
Problem 4
Two similar triangles have areas 9 cm2 and 81 cm2. Find the scale factor between them.
Worked answer
3
k2 = 819 = 9
k = 3
Problem 5
Find the distance between (2, 5) and (2, 12).
Worked answer
7
It is a vertical segment
12 - 5 = 7
No square root needed
Problem 6
Solve x2 = 81.
Worked answer
9 and -9
x = ± 9
Problem 7
Evaluate 161/2.
Worked answer
4
√16 = 4
Problem 8
Two similar triangles have areas 9 and 81. Find the ratio of their sides.
Worked answer
1:3
k2 = 9
k = 3, so sides are 1:3