Given, The inequality is: k<(√2+1)3<k+2, where k is a natural number. We need to compute (√2+1)3 (√2+1)3=2√2+6+3√2+1=5√2+7 Approximating √2≈1.414, we find: 5√2+7≈5×1.414+7=7.07+7=14.07 The inequality becomes: k<14.07<k+2 This implies that k>12.07\ ), so the smallest integer value of k is: k=13 ∴ The value of k is 13 .