Leah was asked to subtract 57–√−27–√ . The following is her work: 57–√−27–√=30–√=0 Find the mistake in Leah’s work. Explain what she did wrong.

Answer 1

Leah's mistake lies in her incorrect handling of the square roots and the subtraction of the two square roots.

1. Leah starts with the expression \( \sqrt{57} - \sqrt{27} \).
2. She incorrectly simplifies \( \sqrt{57} - \sqrt{27} \) directly to \( \sqrt{30} \), which is not correct.

The correct process to handle \( \sqrt{57} - \sqrt{27} \) is:

• First, calculate the square roots individually:

  \(\sqrt{57}\) (approximately 7.55),

  \(\sqrt{27}\) (which simplifies to \(3\sqrt{3}\) or approximately 5.20).

Then, you find the difference:

\( \sqrt{57} - \sqrt{27} \approx 7.55 - 5.20 = 2.35\).

Thus, it is incorrect to combine the square roots as she did; square roots do not combine this way like regular numbers. Therefore, her final result of \(0\) is incorrect, as she did not perform the necessary calculations correctly. The correct representation of square roots does not allow direct subtraction unless both roots are to same base.

In summary, Leah made an error by erroneously assuming the subtraction of square roots could be simplified to a single square root value. The actual subtraction needs to be done separately and calculated numerically if exact values are necessary.