How do you simplify the square root of 72?

There are many techniques for simplifying the square roots. Here √72 can be simplified in the following ways

  • First step is to rewrite the number or expression under the square root in terms of its factors

√72=√12⋅6

=√(4⋅3)⋅(2⋅3)

=√((2⋅2)⋅3)⋅(2⋅3)

=√2⋅2⋅2⋅3⋅3

  • Next we have to take perfect square factors.

√2⋅2⋅2⋅3⋅3→√2⋅2⋅2⋅3⋅3, where 2 and 3 are perfect square factors

→2⋅3√2⋅2⋅2⋅3⋅3

  • Eliminate perfect square factors from under the square root

2⋅3√2⋅2⋅2⋅3⋅3→ 2⋅3√2⋅2⋅2⋅3⋅3

→2⋅3√2

This is the square root of 72 i.e √72=2⋅3√2.

  • Simplyfly again

√72=2⋅3√2

=6√2

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