substitute the values into the pythagorean theorem and simplify.

$(7)^2 + (\sqrt{42})^2 \text{ ? } (\sqrt{86})^2$

$\text{? } = \text{ } + \text{ }$

Question

substitute the values into the pythagorean theorem and simplify.

$(7)^2 + (\sqrt{42})^2 \text{ ? } (\sqrt{86})^2$

$\text{? } = \text{ } + \text{ }$

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "blank_filling_formatter", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [ "Pythagorean Theorem" ], "new_concepts": [], "current_concepts": [ "Pythagorean Theorem" ] } ## Simplify the squared terms $$ \begin{aligned} (7)^2 &= 49 \ (\sqrt{42})^2 &= 42 \ (\sqrt{86})^2 &= 86 \end{aligned} $$ ## Compare the sum of the legs to the hypotenuse squared $$ \begin{aligned} 49 + 42 &= 91 \ 91 &> 86 \end{aligned} $$ ## Fill in the corresponding blanks $$ \begin{aligned} \text{First blank (leftmost): } & 49 \ \text{Second blank (middle): } & 42 \ \text{Third blank (rightmost): } & 86 \ \text{Comparison operator: } & > \end{aligned} $$ Substitute the values into the Pythagorean Theorem and simplify. 49 + 42 $>$ 86 $ (7)^2 + (\sqrt{42})^2 $ $>$ $ (\sqrt{86})^2 $ { "subject": "Mathematics", "question_type": "Fill-in-the-blank", "knowledge_point": [ "Mathematics", "Geometry", "Pythagorean Theorem" ] }

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QUESTION IMAGE

Question

Explanation:

Simplify the squared terms

Compare the sum of the legs to the hypotenuse squared

Fill in the corresponding blanks

Answer: