Root Proof

About This Worksheet

This worksheet helps seventh-grade students choose the correct square root from several answer choices and then prove that the answer is right. Each problem gives a perfect-square value under a radical, followed by several possible roots. Students select the correct value and then write a multiplication fact to check it. This makes the worksheet more thoughtful than a simple matching page because students must support the answer with evidence. It helps them understand that a square root is the number that multiplies by itself to make the original value.

What Students Practice

Students evaluate square roots such as √16, √25, √36, √49, √64, √81, √100, √121, √144, and √169. After choosing the correct answer, they verify it by multiplying the root by itself. This gives them repeated practice with radical notation, perfect squares, multiplication facts, and mathematical checking. The multiple-choice format also asks students to compare reasonable and unreasonable options rather than just recall a fact from memory. That extra check helps strengthen number sense.

Why This Matters

Students sometimes guess a square root because the numbers look familiar, but this worksheet teaches them how to prove the answer. For example, if they believe √81 = 9, they can check by showing that 9 × 9 = 81. That habit builds confidence because students do not have to rely only on memorization. It also prepares them for later square-root estimation, where knowing nearby perfect-square facts becomes very important. The check step encourages students to become more independent problem solvers.

Teaching Tips

Ask students to circle an answer only after they can name the multiplication fact that proves it. If they are unsure, have them test the answer choices by multiplying each possible root by itself. Encourage them to write the check clearly, such as “11 × 11 = 121.” This is a good opportunity to remind students that the worksheet is asking for the positive square root. Over time, they should begin recognizing these common roots more quickly.

Curriculum Standards

This worksheet builds Grade 7 readiness for CCSS.MATH.CONTENT.8.NS.A.2, where students work more formally with square roots and irrational numbers. The verification step also supports mathematical reasoning because students justify an answer with a multiplication fact. It strengthens perfect-square fluency and prepares students for later estimation and comparison of radicals. The page works well for class practice, homework, intervention, or review.