Square Roots

Sidekick Check

Student Summary

We know that:

  • 9=3\sqrt{9}=3 because 32=93^2=9.

  • 16=4\sqrt{16}=4 because 42=164^2=16.

The value of 10\sqrt{10} must be between 3 units and 4 units because it is between the values of 9\sqrt{9} and 16\sqrt{16}.

There are 3 squares on a square grid, arranged in order of area, from smallest, on the left, to largest, on the right.
There are 3 squares on a square grid, arranged in order of area, from smallest, on the left, to largest, on the right. The left most square is aligned to the grid and has side lengths of 3 with an area of 9. The middle square is tilted on the grid so that its sides are diagonal to the grid. The square is labeled with a side length of square root of 10 and an area of 10. The right most square is aligned to the grid and has side lengths of 4 with an area of 16.

Visual / Anchor Chart

Standards

Building On
8.G.2

Know that a two-dimensional figure is congruent to another if the corresponding angles are congruent and the corresponding sides are congruent. Equivalently, two two-dimensional figures are congruent if one is the image of the other after a sequence of rotations, reflections, and translations. Given two congruent figures, describe a sequence that maps the congruence between them on the coordinate plane.

Addressing
8.EE.2

Use square root and cube root symbols to represent solutions to equations of the form x^2 = p and x^3 = p, where p is a positive rational number. Know square roots of perfect squares up to 225 and cube roots of perfect cubes up to 125. Know that the square root of a non-perfect square is irrational.

8.F.B

No additional information available.

Building Toward
8.G.7

Apply the Pythagorean Theorem to determine unknown side lengths in right triangles in real world and mathematical problems in two and three dimensions.