Order the following expressions: a = 6^(1)/(3), b = 2 sqrt(2), and c = 1.22.

May 7, 2026Mathematics

ScanSolve AI Answer

May 7, 2026

Answer

b < c < a

To order $a, b,$ and $c$ , we need to calculate the numerical value of each expression.

Step 1: Calculate the value of $a$ . $a = 6^{\frac{1}{3}}$ This means $a$ is the cube root of 6. We know that $1^3 = 1$ and $2^3 = 8$ . So, $a$ must be between 1 and 2. A calculator gives $a \approx 1.817$ .

Step 2: Calculate the value of $b$ . $b = \log_2 \sqrt{2}$ We can rewrite $\sqrt{2}$ as $2^{\frac{1}{2}}$ . Using the logarithm property $\log_x x^y = y$ : $b = \log_2 2^{\frac{1}{2}}$ $b = \frac{1}{2}$ $b = 0.5$

Step 3: Calculate the value of $c$ . $c = 1.2^2$ $c = 1.2 \times 1.2$ $c = 1.44$

Step 4: Compare the values of $a, b,$ and $c$ . We have: $a \approx 1.817$ $b = 0.5$ $c = 1.44$

Arranging these values in ascending order: $0.5 < 1.44 < 1.817$ So, $b < c < a$ .

The ordering of $a, b, c$ is $\boxed{b < c < a}$ . Last free one today — make it count tomorrow, or type /upgrade for unlimited.

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Quick Answer

To order a, b, and c, we need to calculate the numerical value of each expression.

Asked on May 7, 2026Mathematics

This mathematics problem involves applying core mathematical principles and formulas. Below you will find a complete step-by-step solution with detailed explanations for each step, helping you understand not just the answer but the method behind it.

ScanSolve AI AnswerAnswered on May 7, 2026

To order a, b, and c, we need to calculate the numerical value of each expression. Step 1: Calculate the value of a. a = 6^(1)/(3) This means a is the cube root of 6. We know that 1^3 = 1 and 2^3 = 8. So, a must be between 1 and 2. A calculator gives a ≈ 1.817. Step 2: Calculate the value of b. b = _2 sqrt(2) We can rewrite sqrt(2) as 2^(1)/(2). Using the logarithm property _x x^y = y: b = _2 2^(1)/(2) b = (1)/(2) b = 0.5 Step 3: Calculate the value of c. c = 1.2^2 c = 1.2 × 1.2 c = 1.44 Step 4: Compare the values of a, b, and c. We have: a ≈ 1.817 b = 0.5 c = 1.44 Arranging these values in ascending order: 0.5 < 1.44 < 1.817 So, b < c < a. The ordering of a, b, c is b < c < a. Last free one today — make it count tomorrow, or type /upgrade for unlimited.