Question

A radical (square root of a number) is said to be in simplest form when all perfect squares have been factored out and simplified: sqrt 32 can be factored as sqrt 16.2 which we can simplify to sqrt16 sqrt2 which we can simplify again to 4sqrt2. What are the first 20 perfect squares?

Answer 1

The first 20 perfect squares are the squares of the whole numbers from 1 to 20. They are important for various mathematical calculations, especially for simplifying radical expressions.

Step-by-step explanation:

Understanding Perfect Squares

The first 20 perfect squares are the squares of the first 20 whole numbers. These numbers are important because they come up frequently in various mathematical calculations, especially in problems involving area and rooting. A perfect square is the result of a number multiplied by itself. For example, the square of 4 is 16, because 4 times 4 equals 16.

1 (1x1)

4 (2x2)

9 (3x3)

16 (4x4)

25 (5x5)

36 (6x6)

49 (7x7)

64 (8x8)

81 (9x9)

100 (10x10)

121 (11x11)

144 (12x12)

169 (13x13)

196 (14x14)

225 (15x15)

256 (16x16)

289 (17x17)

324 (18x18)

361 (19x19)

400 (20x20)

Knowing these perfect squares helps with simplifying radical expressions, like converting sqrt(32) to 4sqrt(2) by recognizing that 32 is 16 times 2, as in the illustration given.