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Grade 7 · Number · Powers, Squares, and Large Numbers

Use Powers and Square Roots

Powers write repeated multiplication compactly. Perfect squares and their square roots connect that notation to the geometry of a square.

The big idea

An exponent describes repeated factors

In 10⁶, the exponent 6 means six factors of 10. In 9², the exponent 2 means 9 × 9, while √81 reverses the operation and asks which positive number squares to 81.

Work it through

Represent 307,020,050 and find √144

  1. 1. Match each non-zero digit to its place value.
  2. 2. Write 307,020,050 as 3 × 10⁸ + 7 × 10⁶ + 2 × 10⁴ + 5 × 10.
  3. 3. Recognize 144 as 12 × 12.
  4. 4. Therefore √144 = 12.