QuestionSimplify: (2+√10)(7+√10). Choose one: a. 14+2√10 b. 24+9√10 c. 14+9√10 d. 114+9√10

Studdy Solution

STEP 1

Assumptions1. We are given the expression $(+\sqrt{10})(7+\sqrt{10})$ and asked to simplify it completely. . We will use the distributive property of multiplication over addition to simplify the expression.

STEP 2

The distributive property of multiplication over addition states that for any real numbers a, b, and c, the equation $(a + b) \cdot c = a \cdot c + b \cdot c$ holds true. We will apply this property to our expression.
$(2+\sqrt{10})(7+\sqrt{10}) =2 \cdot7 +2 \cdot \sqrt{10} + \sqrt{10} \cdot7 + \sqrt{10} \cdot \sqrt{10}$

STEP 3

Now, we simplify the above expression by performing the multiplication operations.
$=14 +2\sqrt{10} +7\sqrt{10} +10$

STEP 4

Next, we combine like terms.
$=24 +9\sqrt{10}$ So, the simplified form of the given expression is $24 +9\sqrt{10}$ .
Therefore, the correct answer is option b. $24 +9\sqrt{10}$ .

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