Questions: Multiply and simplify the following radical expressions. (sqrt7-5)(sqrt7-6)

Multiply and simplify the following radical expressions. (sqrt7-5)(sqrt7-6)
Transcript text: Multiply and simplify the following radical expressions. \[ (\sqrt{7}-5)(\sqrt{7}-6) \]
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Solution

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Solution Steps

Step 1: Expand the expression using FOIL

We multiply the two binomials using the FOIL method (First, Outer, Inner, Last): $(\sqrt{7}-5)(\sqrt{7}-6) = (\sqrt{7})(\sqrt{7}) + (\sqrt{7})(-6) + (-5)(\sqrt{7}) + (-5)(-6)$

Step 2: Simplify the terms

$(\sqrt{7})(\sqrt{7}) + (\sqrt{7})(-6) + (-5)(\sqrt{7}) + (-5)(-6) = 7 - 6\sqrt{7} - 5\sqrt{7} + 30$

Step 3: Combine like terms

$7 - 6\sqrt{7} - 5\sqrt{7} + 30 = 37 - 11\sqrt{7}$

Final Answer:

$37 - 11\sqrt{7}$

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