Simplify $\sqrt{2} \times 2 \sqrt{2}$
Answer (2)
Rewrite the expression: 2 ( 2 2 ) .
Simplify the square roots: 2 2 = 2 .
Multiply the remaining numbers: 22 = 4 .
The simplified expression is 4 .
Explanation
Understanding the Problem We are asked to simplify the expression 2 × 2 2 . This involves multiplying a number by a square root and then multiplying by another square root.
Rewriting the Expression First, we can rewrite the expression to group the square roots together: 2 × ( 2 × 2 )
Simplifying Square Roots Next, we simplify the product of the square roots. Recall that a × a = a . Therefore, 2 × 2 = 2 . So our expression becomes: 2 × 2
Final Calculation Finally, we multiply the remaining numbers: 2 × 2 = 4
Conclusion Thus, the simplified expression is 4 .
Examples
Understanding how to simplify expressions with square roots is useful in many areas, such as physics and engineering. For example, when calculating the length of the diagonal of a square with side length 2 , you would use the Pythagorean theorem: d 2 = ( 2 ) 2 + ( 2 ) 2 = 2 + 2 = 4 , so d = 4 = 2 . Simplifying radical expressions helps in finding exact values in geometric and scientific problems.
The simplified form of 2 × 2 2 is 4 . This is achieved by rewriting the expression and using the property of square roots. After simplification, the final answer is 4 .
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